We investigate the late Miocene‐Pleistocene offshore sedimentary record of the Yakutat microplate to evaluate the spatial and temporal variations in rock exhumation and sediment routing patterns at the heavily glaciated and actively converging plate boundary in southeast Alaska. We present 1,456 new fission track ages and 1,372 new U‐Pb ages from double‐dated detrital zircons derived from fourteen samples collected from offshore. We integrate our results with published geochronology and thermochronology data onland and offshore in order to constrain grain provenance. We find that offshore strata deposited east of the fold and thrust belt are sourced from the rapidly exhuming areas along the entire Fairweather Fault, the northeastern part of the syntaxial region, as well as the slowly exhuming Insular superterrane. In contrast, the western strata are sourced from the emerging fold and thrust belt and the Chugach Metamorphic Complex located north of the plate boundary. In these samples we identified a change in sediment provenance, which we suggest marks the capture of the Bagley Ice Valley by the proto‐Bering Glacier at the transition from the early to late Pliocene. This implies that the modern Bagley‐Bering Glacier System is much older than previously known. Strata deposited at ~8.6 Ma suggest that extreme rapid exhumation was already ongoing in the late Miocene, which supports previous findings in deep‐sea deposits. Overall, the data help discern several stages in the evolution of sediment routing patterns in response to dynamic tectonic and surficial processes along this active convergent margin.