The remarkable cell diversity of multicellular organisms relies on the ability of multipotent progenitor cells to generate distinct cell types at the right times and locations during embryogenesis. A key question is how progenitors establish competence to respond to the different environmental signals required to produce specific cell types at critical developmental timepoints. We addressed this in the mouse developing forebrain, where neural progenitor cells must switch from producing neurons to making oligodendrocytes in response to increased Sonic Hedgehog (SHH) signaling during late embryogenesis. We show that progenitor responses to SHH are regulated by Notch signaling, thus permitting proper timing of the neuron-oligodendrocyte switch. Notch activity epigenetically primes genes associated with the oligodendrocyte lineage and SHH pathway, enabling amplified transcriptional responses to endogenous SHH and robust oligodendrogenesis. These results reveal a critical role for Notch in facilitating progenitor competence states and influencing cell fate transitions at the epigenetic level.