<PAGE>

                                                                   EXHIBIT 3.1.3


                    CERTIFICATE OF DESIGNATIONS, PREFERENCES
                                 AND RIGHTS OF
                      SERIES B CONVERTIBLE PREFERRED STOCK
                                       OF
                            TRANSCEND SERVICES, INC.

                     Pursuant to Section 151 of the General
                    Corporation Law of the State of Delaware

     Transcend Services, Inc., a corporation organized and existing under the
General Corporation Law of the State of Delaware (the "Corporation"), does
hereby certify that, pursuant to the authority contained in paragraph IV of its
Certificate of Incorporation and in accordance with Section 151 of the General
Corporation Law of the State of Delaware, the following resolutions creating a
series of Preferred Stock, $.01 par value, designated as Series B Convertible
Preferred Stock, were duly adopted by the Board of Directors of the Corporation
(the "Board") as of November 10, 1999:

     RESOLVED, that the Board hereby creates from among the Corporation's
21,000,000 authorized and previously undesignated shares of Preferred Stock,
$.01 par value, a series of such Preferred Stock to be known as the "Series B
Convertible Preferred Stock" and to comprise 60,000 shares, and hereby adopts
and prescribes therefore the designation, relative rights, preferences and
limitations, and other terms and conditions of such series as set forth in, and
governed by, Exhibit A attached to these minutes, with such Exhibit A being
hereby incorporated as part of this resolution; and

     FURTHER RESOLVED, that the officers of the Corporation be and hereby are
authorized and directed to take any and all further action that may be necessary
or desirable to accomplish the above authorized action, including but not
limited to the execution and filing of all instruments or documents that may be
necessary to create, designate, issue or evidence shares of the Corporation's
Series B Convertible Preferred Stock.

     IN WITNESS WHEREOF, the Corporation has caused this Certificate to be
executed in its name by the undersigned duly authorized officer of the
Corporation, this 12th day of January, 2000.

                                By:   /s/ Larry G. Gerdes
                                   -----------------------------------------
                                        Larry G. Gerdes

                                Title: President and Chief Executive Officer

ATTEST:

By:       Doug Shamon
   --------------------------------
Title:    Exec. VP, Chief Financial Officer
      ---------------------------------------
<PAGE>

                                                                       EXHIBIT A

                      SERIES B CONVERTIBLE PREFERRED STOCK

     1.   Designation; Rank. 60,000 shares of the preferred stock, $.01 par
          -----------------
value, stated value $25.00 per share (the "Stated Value"), of the Corporation
are hereby constituted as a series of the preferred stock designated as "Series
B Convertible Preferred Stock" (the "Series B Preferred Stock") and having
relative rights and preferences to all other classes and series of the capital
stock of the Corporation as set forth herein.  The Series B Preferred Stock
shall rank junior to the Corporation's Series A Preferred Stock and senior to
all other classes or series of capital stock of the Corporation except as
permitted by Section 4(b) hereof.

     2.   Dividends.     The holders of the Series B Preferred Stock shall not
          ---------
be entitled to receive dividends.

     3.   Preference on Liquidation.
          -------------------------

          (a) Liquidation Preference for Series B Preferred Stock.  In the event
              ---------------------------------------------------
that the Corporation shall commence a voluntary case under the federal
bankruptcy laws or any other applicable federal or state bankruptcy, insolvency
or similar law, or consent to the entry of an order for relief in an involuntary
case under such law or to the appointment of a receiver, liquidator, assignee,
custodian, trustee, sequestrator (or other similar official) of the Corporation
or of any substantial part of its property, or make an assignment for the
benefit of its creditors, or admit in writing its inability to pay its debts
generally as they become due, or if a decree or order for relief in respect of
the Corporation shall be entered by a court having jurisdiction in the premises
in an involuntary case under the federal bankruptcy laws or any other applicable
federal or state bankruptcy, insolvency or similar law, or appointing a
receiver, liquidator, assignee, custodian, trustee, sequestrator (or other
similar official) of the Corporation or of any substantial part of its property,
or ordering the winding up or liquidation of its affairs, and on account of any
such event the Corporation shall liquidate, dissolve or wind up, or if the
Corporation shall otherwise liquidate, dissolve or wind up, no distribution of
the assets of the Corporation shall be made to the holders of shares of Common
Stock or other Junior Securities (and no monies shall be set apart for such
purpose) unless prior thereto, the holders of shares of Series B Preferred Stock
shall have received from the assets of the Corporation an amount per share equal
to the sum of $25.00 (the "Series B Liquidation Preference").

          (b) Pro Rata Payments.  If, upon any such liquidation, dissolution or
              -----------------
other winding up of the affairs of the Corporation, the assets of the
Corporation shall be insufficient to permit the payment in full of the Series B
Liquidation Preference for each share of Series B Preferred Stock then
outstanding and the full liquidating payments on all Parity Securities, then the
assets of the Corporation remaining after the distribution to holders of any
Senior Securities of the full amounts to which they may be entitled shall be
ratably distributed among the holders of Series B Preferred Stock and of any
Parity Securities in proportion to the full amounts to which they would
otherwise be respectively entitled if all amounts thereon were paid in full.
<PAGE>

          (c) Sale not a Liquidation.  Neither the voluntary sale, conveyance,
              ----------------------
exchange or transfer (for cash, shares of stock, securities or other
consideration) of all or substantially all the property or assets of the
Corporation nor the consolidation, merger or other business combination of the
Corporation with or into one or more corporations shall be deemed to be a
liquidation, dissolution or winding up, voluntary or involuntary, of the
Corporation.

          (d) Notice of Liquidation.  Written notice of any liquidation,
              ---------------------
dissolution or winding up of the Corporation, stating the payment date or dates
when and the place or places where amounts distributable in such circumstances
shall be payable, shall be given by first class mail, postage prepaid, not less
than thirty (30) days prior to any payment date specified therein, to the
holders of record of the Series B Preferred Stock at their respective addresses
as shall appear on the records of the Corporation.

     4.   Voting.
          ------

          (a) General Rights.  In addition to any voting rights provided in the
              --------------
Certificate of Incorporation or By-laws, the Series B Preferred Stock shall vote
together with the Common Stock as a single class on all actions to be voted on
by the stockholders of the Corporation.  Each share of Series B Preferred Stock
shall entitle the holder thereof to such number of votes per share on each such
action as shall equal the number of shares of Common Stock (rounded down to the
nearest whole share of Common Stock) into which each share of Series B Preferred
Stock is then convertible.  The holders of Series B Preferred Stock shall be
entitled to notice of any stockholders' meeting in accordance with the By-Laws
of the Corporation.

          (b) Special Voting Rights on Certain Corporate Actions.  The
              --------------------------------------------------
Corporation shall not, without the prior consent (in addition to any other vote
or consent required by law, contract or otherwise) of the holders of seventy-
five percent (75%) of the outstanding shares of Series B Preferred Stock, voting
as a class in person or by proxy in writing or at a special meeting called for
the purpose: (i) create or authorize any additional stock or any class or series
unless the same ranks junior to the Series B Preferred Stock as to dividends, as
to redemptions and as to the distribution of assets on dissolution, liquidation
or winding up, whether voluntary or involuntary, or create or authorize any
obligation or security convertible into shares of stock of any class or series
unless the same ranks junior to the Series B Preferred Stock as to dividends, as
to redemptions and as to the distribution of assets on dissolution, liquidation
or winding up, whether voluntary or involuntary, whether any such creation or
authorization shall be by means of amendment of the Certificate of
Incorporation, this Certificate of Designations, merger, consolidation or
otherwise; or (ii) amend, alter or repeal the Certificate of Incorporation, this
Certificate of Designations or Bylaws, or file any directors' resolutions
pursuant to the General Corporation Law of the State of Delaware, containing, in
any such case, any provision which in any manner adversely affects the
respective powers, designations, preferences or rights, or the qualifications,
limitations or restrictions thereof, of the Series B Preferred Stock, (iii)
agree to, or permit any subsidiary to agree to, any provision in any agreement
that would impose any restrictions on the Corporation's right to make any
redemption of or convert any of the Series B

                                      -3-
<PAGE>

Preferred Shares or otherwise prohibit the Corporation from honoring the
exercise of any rights the holders of the Series B Preferred Shares now have or
may hereafter have, or (iv) engage in any merger, share exchange, consolidation
or reorganization which would result in the holders of Common Stock of the
Corporation immediately prior to such transaction owning less than fifty percent
(50%) of the Common Stock of the Corporation, or such surviving entity,
immediately after such transaction.

     5.   Conversion.  The holders of Series B Preferred Stock shall have the
          ----------
right to convert all or a portion of such shares into fully paid and
nonassessable shares of Common Stock or any capital stock or other securities
into which such Common Stock shall have been changed or any capital stock or
other securities resulting from a reclassification thereof as follows:

          (a) Optional Conversion.  Subject to and upon compliance with the
              -------------------
provisions of this Section 5, a holder of shares of Series B Preferred Stock
shall have the right without payment of any additional consideration, at the
option of such holder, at any time or from time to time, to convert each of such
shares into the number of fully paid and nonassessable shares of Common Stock
(calculated as to each conversion to the nearest 1/100th of a share of Common
Stock) obtained by dividing $25.00 by the Conversion Price then in effect and by
surrender of such shares, such surrender to be made in the manner provided in
paragraph (b) of this Section 5.  The Common Stock issuable upon conversion of
the shares of Series B Preferred Stock, when such Common Stock shall be issued
in accordance with the terms hereof, are hereby declared to be and shall be duly
authorized, validly issued, fully paid and nonassessable Common Stock held by
the holders thereof.

          (b) Mechanics of Conversion.  Each holder of Series B Preferred Stock
              -----------------------
that desires to convert the same into shares of Common Stock shall surrender the
certificate or certificates therefor, duly endorsed, at the principal office of
the Corporation or of any transfer agent for the Series B Preferred Stock or
Common Stock, accompanied by written notice to the Corporation setting forth the
name or names in which such holder wishes the certificate or certificates for
shares of Common Stock to be issued if such name or names shall be different
than that of such holder.  In case such notice shall specify a name or names
other than that of such holder, such notice shall be accompanied by payment of
all transfer taxes payable upon the issuance and delivery of shares of Common
Stock in such name or names.  Thereupon, the Corporation shall issue and deliver
at such office on the fifth (5th) succeeding Business Day (unless such
conversion is in connection with an underwritten public offering of Common
Stock, in which event concurrently with such conversion) to such holder or on
such holder's written order, (i) a certificate or certificates for the number of
validly issued, fully paid and nonassessable full shares of Common Stock to
which such holder is entitled and (ii) if less than the full number of shares of
Series B Preferred Stock evidenced by the surrendered certificate or
certificates are being converted, a new certificate or certificates, of like
tenor, for the number of shares evidenced by such surrendered certificate or
certificates less the number of shares converted.

                                      -4-
<PAGE>

          Each conversion shall be deemed to have been effected immediately
prior to the close of business on the date of such surrender of the shares to be
converted (except that if such conversion is in connection with an underwritten
public offering of Common Stock, then such conversion shall be deemed to have
been effected upon such surrender) so that the rights of the holder thereof as
to the shares being converted shall cease at such time except for the right to
receive shares of Common Stock, and the person entitled to receive the shares of
Common Stock issuable upon such conversion shall be treated for all purposes as
the record holder of such shares of Common Stock at such time.

          (c) Adjustment of the Conversion Price.  The Conversion Price shall be
              ----------------------------------
adjusted from time to time as follows:

               (i)   Adjustment for Stock Splits and Combinations.  If the
                     --------------------------------------------
          Corporation at any time or from time to time after the Issue Date
          effects a subdivision of the outstanding Common Stock or combines the
          outstanding shares of Common Stock, then, in each such case, the
          Conversion Price in effect immediately prior to such event shall be
          adjusted so that each holder of shares of Series B Preferred Stock
          shall have the right to convert its shares of Series B Preferred Stock
          into the number of shares of Common Stock which it would have owned
          after the event had such shares of Series B Preferred Stock been
          converted immediately before the happening of such event. Any
          adjustment under this Section 5(c)(i) shall become effective as of the
          date and time the subdivision or combination becomes effective.

               (ii)  Reorganization, Reclassification, Merger or Consolidation.
                     ---------------------------------------------------------
          If the Corporation shall at any time reorganize or reclassify the
          outstanding shares of Common Stock (other than a change in par value,
          or from no par value to par value, or from par value to no par value,
          or as a result of a subdivision or combination) or consolidate with or
          merge into another corporation (where the Corporation is not the
          continuing corporation after such merger or consolidation), the
          holders of Series B Preferred Stock shall thereafter be entitled to
          receive upon conversion of the Series B Preferred Stock in whole or in
          part, the same kind and number of shares of stock and other
          securities, cash or other property (and upon the same terms and with
          the same rights) as would have been distributed to a holder upon such
          reorganization, reclassification, consolidation or merger had such
          holder converted its Series B Preferred Stock immediately prior to
          such reorganization, reclassification, consolidation or merger
          (subject to subsequent adjustments under Section 5(c) hereof). The
          Conversion Price upon such conversion shall be the Conversion Price
          that would otherwise be in effect pursuant to the terms hereof.
          Notwithstanding anything herein to the contrary, the Corporation will
          not effect any such reorganization, reclassification, merger or
          consolidation unless prior to the consummation thereof, the
          corporation who may be required to deliver any stock, securities or

                                      -5-
<PAGE>


          other assets upon the conversion of the Series B Preferred Stock shall
          agree by an instrument in writing to deliver such stock, cash,
          securities or other assets to the holders of the Series B Preferred
          Stock. A sale, transfer or lease of all or substantially all of the
          assets of the Corporation to another person shall be deemed a
          reorganization, reclassification, consolidation or merger for the
          foregoing purposes.

               (iii) Issuance of Common Stock at a Price Below Conversion
                     ----------------------------------------------------
          Price.  In case the Corporation at any time or from time to time shall
          ------
          issue after the Issue Date shares of its Common Stock (or securities
          convertible into its Common Stock) at a price per share (or having a
          conversion price per share) less than the Conversion Price (as defined
          in Section 8 below) per share of Common Stock, and in such case, the
          number of shares of Common Stock into which each share of the Series B
          Preferred Stock is convertible shall be adjusted so that the holder of
          each share thereof shall be entitled to receive, upon the conversion
          thereof, the number of shares of Common Stock determined by
          multiplying (a) the number of shares of Common Stock into which such
          share was convertible immediately prior to such event by (b) a
          fraction, the numerator of which shall be the sum of (I) the number of
          shares of Common Stock outstanding immediately prior to such event
          plus (II) the number of additional shares of Common Stock issued, and
          the denominator of which shall be the sum of (III) the number of
          shares of Common Stock outstanding immediately prior to such event
          plus (IV) the number of shares of Common Stock which the aggregate
          consideration receivable by the Corporation for the total number of
          shares of Common Stock so issued would purchase at such Conversion
          Price on the date of such issuance. The adjustment contemplated by
          this section shall not be made for the first 250,000 shares of Common
          Stock issued upon exercise of stock options granted to employees or
          non-employee directors pursuant to plans in existence on the Issue
          Date provided, however, that the consideration received by the
          Corporation upon issuance is at least $2.00 per share.

                (iv) Other Provisions Applicable to Adjustments under this
                     -----------------------------------------------------
          Section.  The following provisions shall be applicable to the making
          -------
          of adjustments of the shares of Common Stock into which the Series B
          Preferred Stock is convertible and the Conversion Price at which the
          Series B Preferred Stock is convertible provided for in this Section
          5(c):

                         (A) When Adjustments to Be Made.  The adjustments
                             ---------------------------
                     required by this Section 5(c) shall be made whenever and as
                     often as any event requiring an adjustment shall occur,
                     except that any adjustment of the Conversion Price that
                     would otherwise be required may be postponed (except in the
                     case of a subdivision or combination of shares of the
                     Common Stock, as provided for in Section 5(c)(i)) up to,
                     but not beyond the date of conversion if such adjustment
                     either by itself or with other adjustments not previously
                     made amount to a change in the Conversion Price is less
                     than $.05. Any adjustment

                                      -6-
<PAGE>

                     representing a change of less than such minimum amount
                     (except as aforesaid) which is postponed shall be carried
                     forward and made as soon as such adjustment, together with
                     other adjustments required by this Section 5(c) and not
                     previously made, would result in a minimum adjustment or on
                     the date of conversion. For the purpose of any adjustment,
                     any event shall be deemed to have occurred at the close of
                     business on the date of its occurrence.

                         (B) Fractional Interests.  In computing adjustments
                             --------------------
                     under this Section 5(c), fractional interests in the Common
                     Stock shall be taken into account to the nearest 1/10th of
                     a share.

                         (C) Challenge to Good Faith Determination.  Whenever
                             -------------------------------------
                     the Board shall be required to make a determination in good
                     faith of the fair value of any item under this Section
                     5(c), such determination may be challenged in good faith by
                     a holder of Series B Preferred Stock and any dispute shall
                     be resolved by an investment banking firm of recognized
                     national standing selected by the Corporation and
                     acceptable to such holder. The fees of such investment
                     banker shall be borne by such holder if the Corporation's
                     calculation is determined to be correct and otherwise by
                     the Corporation.

          (d) No Fractional Share Adjustments.  No fractional shares shall be
              -------------------------------
issued upon conversion of the Series B Preferred Stock.  If more than one share
of the Series B Preferred Stock is to be converted at one time by the same
stockholder, the number of full shares issuable upon such conversion shall be
computed on the basis of the aggregate amount of the shares to be converted.
Instead of any fractional shares of Common Stock which would otherwise be
issuable upon conversion of any shares of Series B Preferred Stock, the
Corporation will pay a cash adjustment in respect of such fractional interest in
an amount equal to the same fraction of the Market Price per share of Common
Stock at the close of business on the day of conversion which such fractional
share of Series B Preferred Stock would be convertible into on such date.

          (e) Shares to be Reserved.  The Corporation shall at all times reserve
              ---------------------
and keep available, out of its authorized and unissued stock, solely for the
purpose of effecting the conversion of the Series B Preferred Stock, such number
of shares of Common Stock as shall from time to time be sufficient to effect the
conversion of all of the Series B Preferred Stock from time to time outstanding.
The Corporation shall from time to time, in accordance with the laws of the
State of Delaware, increase the authorized number of shares of Common Stock if
at any time the number of shares of authorized but unissued Common Stock shall
be insufficient to permit the conversion in full of the Series B Preferred
Stock.

          (f) Taxes and Charges.  The Corporation will pay any and all issue or
              -----------------
other taxes that may be payable in respect of any issuance or delivery of shares
of Common Stock on

                                      -7-
<PAGE>

conversion of the Series B Preferred Stock. The Corporation shall not, however,
be required to pay any tax which may be payable in respect of any transfer
involved in the issuance or delivery of Common Stock in a name other than that
of the Series B Preferred Stock, and no such issuance or delivery shall be made
unless and until the Person requesting such issuance has paid to the Corporation
the amount of such tax or has established, to the satisfaction of the
Corporation, that such tax has been paid.

          (g) Closing of Books.  The Corporation will at no time close its
              ----------------
transfer books against the transfer of any shares of Series B Preferred Stock or
of any shares of Common Stock issued or issuable upon the conversion of any
shares of Series B Preferred Stock in any manner which interferes with the
timely conversion of such shares of Series B Preferred Stock.

     6.   Shares to be Retired.  Any share of Series B Preferred Stock
          --------------------
converted, redeemed or otherwise acquired by the Corporation shall be retired
and canceled and shall upon cancellation be restored to the status of authorized
but unissued shares of preferred stock, subject to reissuance by the Board as
shares of preferred stock of one or more other series but not as shares of
Series B Preferred Stock.

     7.   Restrictions on Transfer.  Prior to conversion as set forth in Section
          ------------------------
5, the Series B Preferred Stock shall not be transferrable without the prior
written consent of the Company, which consent shall not be unreasonably
withheld.

     8.   Definitions.  As used herein, the following terms shall have the
          -----------
respective meanings set forth below:

          "Business Day" means any day that is not a Saturday, a Sunday or a day
           ------------
     on which banks are required or permitted to be closed in the State of
     Georgia.

          "Common Stock" means the Corporation's Common Stock, $.01 par value
           ------------
     per share, and any stock into which such Common Stock may hereafter be
     changed or for which such Common Stock may be exchanged after giving effect
     to the terms of such change or exchange (by way of reorganization,
     recapitalization, merger, consolidation or otherwise).

          "Conversion Price" means the Conversion Price per share of Common
           ----------------
     Stock into which the Series B Preferred Stock is convertible, as such
     Conversion Price may be adjusted pursuant to Section 5 hereof. The initial
     Conversion Price shall be the greater of (i) the average closing bid price
     of one share of Common Stock for the five (5) Business Days preceding the
     Issue Date or (ii) the closing bid price of one share of Common Stock on
     the day preceding the Issue Date.

          "Issue Date" means, as to any share of Series B Preferred Stock, the
           ----------
     date of original issuance thereof by the Corporation.

                                      -8-
<PAGE>

          "Junior Securities" means the Common Stock and any other class of
           -----------------
     capital stock or series of preferred stock hereafter created by the
     Corporation which does not expressly provide that it ranks senior to or
     pari passu with the Series B Preferred Stock as to dividends, other
     ---- -----
     distributions, liquidation preference or otherwise.

          "Parity Securities" mean any class of capital stock or series of
           -----------------
     preferred stock hereafter created by the Corporation which expressly
     provides that it ranks pari passu with the Series B Preferred Stock as to
                            ---- -----
     dividends, other distributions, liquidation preference or otherwise.

          "Person" or "person" shall mean an individual, partnership,
           ------      ------
     corporation, trust, unincorporated organization, joint venture, government
     or agency, political subdivision thereof, or any other entity of any kind.

          "Public Equity Offering" means an underwritten offering with gross
           ----------------------
     proceeds to the Corporation of at least $15 million pursuant to a
     registration statement that has been declared effective by the Commission
     (other than a registration statement on Form S-8 or otherwise relating to
     equity securities issuable under any employee benefit plan of the
     Corporation).

          "Senior Securities" means the Corporation's Series A Convertible
           -----------------
     Preferred Stock and any class or series of capital stock, debt instrument
     or security convertible into capital stock or debt securities of the
     Corporation other than Parity Securities or Junior Securities.

          "Series B Liquidation Preference" shall have the meaning set forth in
           -------------------------------
     Section 3(a).

          "Series B Preferred Stock" shall have the meaning set forth in Section
           ------------------------


     9.   Notices.  Except as may otherwise be provided for herein, all notices
          -------
referred to herein shall be in writing, and all notices hereunder shall be
deemed to have been given (i) upon receipt, in the case of a notice of
conversion given to the Corporation as contemplated in Section 5(b) hereof, or
(ii) in all other cases, upon the earlier of (x) receipt of such notice, (y)
three Business Days after the mailing of such notice if sent by registered mail
(unless first-class mail shall be specifically permitted for such notice under
the terms hereof) or (z) the Business Day following sending such notice by
overnight courier, in any case with postage or delivery charges prepaid,
addressed:  if to the Corporation, to its offices at 3353 Peachtree Road, N.E.,
Suite 1000, Atlanta, Georgia 30342, Attention: Douglas A. Shamon, or to an agent
of the Corporation designated as permitted by the Articles of Incorporation, or,
if to any holder of the Series B Preferred Stock, to such holder at the address
of such holder of the Series B Preferred Stock as listed in the stock record
books of the Corporation.

                                      -9-