Cancer stem cells (CSCs) are proposed to drive tumor initiation and progression. Yet, our understanding of the cellular and molecular mechanisms that underlie CSC properties is limited. Here we show that the activity of TAZ, a transducer of the Hippo pathway, is required to sustain self-renewal and tumor-initiation capacities in breast CSCs. TAZ protein levels and activity are elevated in prospective CSCs and in poorly differentiated human tumors and have prognostic value. Gain of TAZ endows self-renewal capacity to non-CSCs. In epithelial cells, TAZ forms a complex with the cell-polarity determinant Scribble, and loss of Scribble--or induction of the epithelial-mesenchymal transition (EMT)--disrupts the inhibitory association of TAZ with the core Hippo kinases MST and LATS. This study links the CSC concept to the Hippo pathway in breast cancer and reveals a mechanistic basis of the control of Hippo kinases by cell polarity.