During continental breakup, the locus of strain shifts from a broad region of border faulting and ductile plate stretching to a narrow zone of magma intrusion in a young ocean basin. Recent studies of volcanic rifts and margins worldwide suggest this shift occurs sub‐aerially, before the onset of seafloor spreading. We test this hypothesis using recently‐acquired seismic reflection and borehole data from the Danakil Depression, Ethiopia, a unique region of transition between continental rifting and seafloor spreading. Our data, located near Dallol, ~30km northwest of the Erta'Ale Volcanic Segment (EAVS), reveal a remarkably‐thick (>1km) sequence of young (~100ka) evaporites in a basin bound by a major (≤400m throw), east‐dipping normal fault. To generate such a large amount of subsidence in such a relatively short time, we propose that upper‐crustal extension in Danakil is currently dominated by faulting, not magmatic intrusion. Given the region's markedly thinned crust (~15‐km‐thick), relative to elsewhere in Afar where magma‐assisted rifting dominates and maintains crustal thickness at ~25km, mechanical extension in Danakil is likely coupled with ductile extension of the lower‐crust and mantle lithosphere. Despite proximity to the voluminous lavas of the active EAVS, evidence for igneous material in the upper ~2km of the 6–10‐km‐wide basin is limited. Late‐stage stretching was likely aided by thermal/strain‐induced lithospheric weakening following protracted magma‐assisted rifting. Basin formation immediately prior to the onset of seafloor spreading may also explain the accumulation of thick marine‐seepage‐fed evaporite sequences akin to those observed, for example, along the South Atlantic rifted margins.