A relatively small number of signaling pathways drive a wide range of developmental decisions, but how this versatility in signaling outcome is generated is not clear. In the Drosophila follicular epithelium, localized epidermal growth factor receptor (EGFR) activation induces distinct cell fates depending on its location. Posterior follicle cells respond to EGFR activity by expressing the T-box transcription factors Midline and H15, while anterior cells respond by expressing the homeodomain transcription factor Mirror. We show that the choice between these alternative outputs of EGFR signaling is regulated by antiparallel gradients of JAK/STAT and BMP pathway activity and that mutual repression between Midline/H15 and Mirror generates a bistable switch that toggles between alternative EGFR signaling outcomes. JAK/STAT and BMP pathway input is integrated through their joint and opposing regulation of both sides of this switch. By converting this positional information into a binary decision between EGFR signaling outcomes, this regulatory network ultimately allows the same ligand-receptor pair to establish both the anterior-posterior (AP) and dorsal-ventral (DV) axes of the tissue.