AbstractTectonic extension of continental lithosphere creates accommodation space in which sediments are deposited. Climate‐driven processes provide the mechanism by which mass is detached from hillslopes and sediments are transported into this accommodation space. These two forcings, climate and tectonics, act together to create either endorheic (internally drained) or exorheic (externally drained) rift basins. Here we use a large‐scale dynamic landscape evolution‐tectonics model to understand the contribution of tectonic processes in endorheic‐exorheic transitions. In the model, extension results in opening of an asymmetric half‐graben along a listric normal fault. Rift opening occurs in the models in wet, temperate, or semiarid climates where runoff and evapotranspiration are varied. Our numerical experiments show that slow rift‐opening rates, a slowing‐down of rift opening, or increase of headwater topography (e.g., upstream epeirogenic uplift), are tectonic situations that can cause a transition from an endorheic to an exorheic drainage state in a rift basin. Our results also show that wet climate conditions lead to a permanent exorheism that persists regardless of rift‐opening rates. In semiarid climates, endorheic conditions are favored and may last for the duration of rifting except for when rift opening is very slow. These results form an interpretive framework to study endorheic and exorheic drainage systems in natural continental rifts. In the slow‐opening Rio Grande rift, the endorheic‐exorheic transition may have occurred without dramatic climate changes. Lake‐level variations in East African rift basins are predicted by our models to result from variations in climate.