The gut epithelium has remarkable self-renewal capacity that under homeostatic conditions is driven by Wnt signalling in Lgr5(+) intestinal stem cells (ISCs). However, the mechanisms underlying ISC regeneration after injury remain poorly understood. The Hippo signalling pathway mediates tissue growth and is important for regeneration. Here we demonstrate in mice that Yap, a downstream transcriptional effector of Hippo, is critical for recovery of intestinal epithelium after exposure to ionizing radiation. Yap transiently reprograms Lgr5(+) ISCs by suppressing Wnt signalling and excessive Paneth cell differentiation, while promoting cell survival and inducing a regenerative program that includes Egf pathway activation. Accordingly, growth of Yap-deficient organoids is rescued by the Egfr ligand epiregulin, and we find that non-cell-autonomous production of stromal epiregulin may compensate for Yap loss in vivo. Consistent with key roles for regenerative signalling in tumorigenesis, we further demonstrate that Yap inactivation abolishes adenomas in the Apc(Min) mouse model of colon cancer, and that Yap-driven expansion of Apc(-/-) organoids requires the Egfr module of the Yap regenerative program. Finally, we show that in vivo Yap is required for progression of early Apc mutant tumour-initiating cells, suppresses their differentiation into Paneth cells, and induces a regenerative program and Egfr signalling. Our studies reveal that upon tissue injury, Yap reprograms Lgr5(+) ISCs by inhibiting the Wnt homeostatic program, while inducing a regenerative program that includes activation of Egfr signalling. Moreover, our findings reveal a key role for the Yap regenerative pathway in driving cancer initiation.