In diffuse large B-cell lymphoma (DLBCL) poor outcome is associated with EIF4B-dependent stimulation of the DEAD box helicase eIF4A that unwinds RNA structures in 5’ untranslated regions (UTRs) in mRNAs that encode proteins with a role in cell proliferation. We carried out iCLIP to examine differences in RNAs bound by eIF4B in DLBCL-derived- versus control B-cells and show that eIF4B bound ~10-fold more mRNAs in DLBCL-derived cells. In addition to interacting with 5' UTRs we unexpectedly find that eIF4B binds across the entire mRNA transcripts, with mutually exclusive, position-dependent binding related to different functional protein groups. Interestingly, there was an enrichment for binding within the 3’ UTR of mRNAs encoding replication-dependent histones, and consistent with this, we find that eIF4B interacts with UPF1, a helicase that plays a key role in the turnover of histone mRNAs at the end of S-phase. We identify a direct role for eIF4B in the turnover of histone mRNAs and demonstrate that eIF4B contributes to regulated cell cycle progression through controlling the translation and turnover of selected mRNAs.