The Hippo signalling pathway restricts cell proliferation in animal tissues by inhibiting Yes-associated protein (YAP or YAP1) and Transcriptional Activator with a PDZ domain (TAZ or WW-domain-containing transcriptional activator WWTR1), coactivators of the Scalloped (Sd or TEAD) DNA-binding transcription factor. Drosophila has a single YAP/TAZ homolog named Yorkie (Yki) that is regulated by Hippo pathway signalling in response to epithelial polarity and tissue mechanics during development. Here, we show that Yki translocates to the nucleus to drive Sd-mediated cell proliferation in the ovarian follicle cell epithelium in response to mechanical stretching caused by the growth of the germline. Importantly, mechanically induced Yki nuclear localisation also requires nutritionally induced insulin/insulin-like growth factor 1 (IGF-1) signalling (IIS) via phosphatidyl inositol-3-kinase (PI3K), phosphoinositide-dependent kinase 1 (PDK1 or PDPK1), and protein kinase B (Akt or PKB) in the follicular epithelium. We find similar results in the developing Drosophila wing, where Yki becomes nuclear in the mechanically stretched cells of the wing pouch during larval feeding, which induces IIS, but translocates to the cytoplasm upon cessation of feeding in the third instar stage. Inactivating Akt prevents nuclear Yki localisation in the wing disc, while ectopic activation of the insulin receptor, PI3K, or Akt/PKB is sufficient to maintain nuclear Yki in mechanically stimulated cells of the wing pouch even after feeding ceases. Finally, IIS also promotes YAP nuclear localisation in response to mechanical cues in mammalian skin epithelia. Thus, the Hippo pathway has a physiological function as an integrator of epithelial cell polarity, tissue mechanics, and nutritional cues to control cell proliferation and tissue growth in both Drosophila and mammals.