During development, the Drosophila wing primordium undergoes a dramatic increase in cell number and mass under the control of the long-range morphogens Wingless (Wg, a Wnt) and Decapentaplegic (Dpp, a BMP). This process depends in part on the capacity of wing cells to recruit neighboring, non-wing cells into the wing primordium. Wing cells are defined by activity of the selector gene vestigial (vg) and recruitment entails the production of a vg-dependent "feed-forward signal" that acts together with morphogen to induce vg expression in neighboring non-wing cells. Here, we identify the protocadherins Fat (Ft) and Dachsous (Ds), the Warts-Hippo tumor suppressor pathway, and the transcriptional co-activator Yorkie (Yki, a YES associated protein, or YAP) as components of the feed-forward signaling mechanism, and we show how this mechanism promotes wing growth in response to Wg. We find that vg generates the feed-forward signal by creating a steep differential in Ft-Ds signaling between wing and non-wing cells. This differential down-regulates Warts-Hippo pathway activity in non-wing cells, leading to a burst of Yki activity and the induction of vg in response to Wg. We posit that Wg propels wing growth at least in part by fueling a wave front of Ft-Ds signaling that propagates vg expression from one cell to the next.