The Cook Inlet in south‐central Alaska contains the early Oligocene to Recent stratigraphic record of a fore‐arc basin adjacent to a shallowly subducting oceanic plateau. Our new measured stratigraphic sections and detrital zircon U‐Pb geochronology and Hf isotopes from Neogene strata and modern rivers illustrate the effects of flat‐slab subduction on the depositional environments, provenance, and subsidence in fore‐arc sedimentary systems. During the middle Miocene, fluvial systems emerged from the eastern, western, and northern margins of the basin. The axis of maximum subsidence was near the center of the basin, suggesting equal contributions from subsidence drivers on both margins. By the late Miocene, the axis of maximum subsidence had shifted westward and fluvial systems originating on the eastern margin of the basin above the flat‐slab traversed the entire width of the basin. These mud‐dominated systems reflect increased sediment flux from recycling of accretionary prism strata. Fluvial systems with headwaters above the flat‐slab region continued to cross the basin during Pliocene time, but a change to sandstone‐dominated strata with abundant volcanogenic grains signals a reactivation of the volcanic arc. The axis of maximum basin subsidence during late Miocene to Pliocene time is parallel to the strike of the subducting slab. Our data suggest that the character and strike‐orientation of the down‐going slab may provide a fundamental control on the nature of depositional systems, location of dominant provenance regions, and areas of maximum subsidence in fore‐arc basins.