Exhibit 10.4

THIS ASSIGNMENT AND ASSUMPTION OF AGREEMENT OF PURCHASE AND SALE (this Assignment) is entered
into as of the 4th day of October, 2010, by and between WELLS CORE OFFICE INCOME OPERATING PARTNERSHIP, L.P., a Delaware limited partnership (Assignor) and WELLS CORE REIT  ROYAL RIDGE V, LLC, a Delaware limited liability
company (Assignee).

RECITALS

WHEREAS, Assignor, as Buyer, has entered into that certain Agreement of Purchase and Sale dated as of
August 5, 2010, as amended by that certain First Amendment to Agreement of Purchase and Sale dated as of September 7, 2010, that certain Second Amendment to Agreement of Purchase and Sale dated as of September 14, 2010, that certain
Third Amendment to Agreement of Purchase and Sale dated as of September 21, 2010, that certain Fourth Amendment to Agreement of Purchase and Sale dated as of September 28, 2010 and that certain Fifth Amendment to Agreement of Purchase and
Sale dated as of October 1, 2010 (as amended, the Purchase Agreement) with BREOF BNK3A ROYAL RIDGE LP, a Delaware limited liability company, with respect to the purchase and sale of certain real property located in the City
of Irving, County of Dallas and State of Texas as more particularly described in the Purchase Agreement.

WHEREAS, pursuant to Section 15.8 of the Purchase Agreement, Assignor wishes to assign, and Assignee wishes
to accept assignment of, and to assume, all of Assignors rights and obligations under the Purchase Agreement.

NOW, THEREFORE, in consideration of Ten and 00/100 ($10.00) Dollars, and other good and valuable consideration, the receipt and legal sufficiency of which is hereby acknowledged, Assignor hereby
assigns to Assignee all of Assignors right, title and interest in and to the Purchase Agreement and Assignee accepts the foregoing assignment and assumes the obligations of Assignor under the Purchase Agreement.

-Signature Page Follows-



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IN
WITNESS WHEREOF, the parties have each caused their duly authorized representatives to execute this Assignment, on behalf of, and as the act of, Assignor and Assignee, respectively, for the purposes set out herein.



| |  |  |  |                                                                                      |  |                                                                                                       |  |                                                                                 
| |  |  |  | ------------------------------------------------------------------------------------ |  | ----------------------------------------------------------------------------------------------------- |  | --------------------------------------------------------------------------------
| |  |  |  | ASSIGNOR:                                                                           
| |  | 
| |  |  |  | WELLS CORE OFFICE INCOME OPERATING
PARTNERSHIP, L.P., a Delaware limited partnership
| |  |  | 
| |  |  |  | By:                                                                                  |  | Wells Core Office Income REIT, Inc., a
Maryland corporation, its general partner                     
| |  |  | 
| |  |  |  |                                                                                      |  | By: /s/ Douglas P. Williams                                                                          
| |  |  |  |                                                                                      |  | Name: Douglas P. Williams                                                                            
| |  |  |  |                                                                                      |  | Title: Executive Vice President                                                                      
| |  | 
| |  |  |  | ASSIGNEE:                                                                           
| |  | 
| |  |  |  | WELLS CORE REIT  ROYAL RIDGE V, LLC, a
Delaware limited liability company          
| |  |  | 
| |  |  |  | By:                                                                                  |  | Wells Core Office Income Operating
Partnership, L.P., a Delaware limited partnership, its sole member
| |  |  |  |                                                                                     
| |  |  |  |                                                                                      |  | By:                                                                                                   |  | Wells Core Office Income REIT, Inc., a Maryland corporation, its general partner
| |  |  |  |                                                                                     
| |  |  |  |                                                                                      |  |                                                                                                       |  | By: /s/ Douglas P. Williams                                                     
| |  |  |  |                                                                                      |  |                                                                                                       |  | Name: Douglas P. Williams                                                       
| |  |  |  |                                                                                      |  |                                                                                                       |  | Title: Executive Vice President