Lineage-committed cells of many tissues exhibit substantial plasticity in contexts such as wound healing and tumorigenesis, but the regulation of this process is not well understood. We identified the Hippo transducer WWTR1/TAZ in a screen of transcription factors that are able to prompt lineage switching of mammary epithelial cells. Forced expression of TAZ in luminal cells induces them to adopt basal characteristics, and depletion of TAZ in basal and/or myoepithelial cells leads to luminal differentiation. In human and mouse tissues, TAZ is active only in basal cells and is critical for basal cell maintenance during homeostasis. Accordingly, loss of TAZ affects mammary gland development, leading to an imbalance of luminal and basal populations as well as branching defects. Mechanistically, TAZ interacts with components of the SWI/SNF complex to modulate lineage-specific gene expression. Collectively, these findings uncover a new role for Hippo signaling in the determination of lineage identity through recruitment of chromatin-remodeling complexes.