Late Cenozoic cooling and changes in glacial–interglacial cycle tempo are thought to increase global rates of erosion starting ~3 million years ago (Ma). Bedrock rivers set rates and patterns of erosion in most landscapes, but constraints on river response to late Cenozoic climate change remain elusive. Here, we determine cosmogenic isotope and luminescence ages of well-preserved bedrock terraces along the Fortymile River (Yukon River basin) to reconstruct an ~5 Myr history of fluvial adjustment to late Cenozoic climate and Yukon River headwater capture at 2.6 Ma. Post-capture Yukon River downcutting lowered the Fortymile River outlet, forcing subsequent bedrock incision throughout the Fortymile basin in two pulses, from 2.4 to 1.8 Ma and at ~1 Ma. These pulses of incision disrupted longer intervals of slow river channel sedimentation under near-consistent climate forcing from 4.8 to 2.4 Ma and from 1.8 to ~1 Ma. The Fortymile River delivers sediment to the Bering Sea, where provenance and accumulation rate changes since 4.3 Ma match observed variations in incision. Our results link alluviation and incision to late Cenozoic climate steadiness and change, respectively, and support the hypothesis that climate-forced changes in precipitation and runoff fundamentally control the pace of river incision and landscape erosion. Increased river incision and landscape erosion can be attributed to late Cenozoic cooling/changes in hydroclimate, according to cosmogenic isotope and luminescence ages of a sequence of bedrock terraces in the Yukon River basin.