We complete the computation of the integral homology of the generalized braid group B associated to an arbitrary irreducible complex reflection group W of exceptional type. In order to do this we explicitly computed the recursively-defined differential of a resolution of Z as a ZB-module, using parallel computing. We also deduce from this general computation the rational homology of the Milnor fiber of the singularity attached to most of these reflection groups. (C) 2017 Elsevier Inc. All rights reserved.