  Determining the distribution of redshifts of galaxies observed by wide-field
photometric experiments like the Dark Energy Survey is an essential component
to mapping the matter density field with gravitational lensing. In this work we
describe the methods used to assign individual weak lensing source galaxies
from the Dark Energy Survey Year 3 Weak Lensing Source Catalogue to four
tomographic bins and to estimate the redshift distributions in these bins. As
the first application of these methods to data, we validate that the
assumptions made apply to the DES Y3 weak lensing source galaxies and develop a
full treatment of systematic uncertainties. Our method consists of combining
information from three independent likelihood functions: Self-Organizing Map
$p(z)$ (SOMPZ), a method for constraining redshifts from galaxy photometry;
clustering redshifts (WZ), constraints on redshifts from cross-correlations of
galaxy density functions; and shear ratios (SR), which provide constraints on
redshifts from the ratios of the galaxy-shear correlation functions at small
scales. Finally, we describe how these independent probes are combined to yield
an ensemble of redshift distributions encapsulating our full uncertainty. We
calibrate redshifts with combined effective uncertainties of $\sigma_{\langle z
\rangle}\sim 0.01$ on the mean redshift in each tomographic bin.
