The Tadjoura rift forms the westernmost edge of the westerly propagating Sheba ridge, between Arabia and Somalia, as it enters into the Afar depression. From structural and remote sensing data sets, the Tadjoura rift is interpreted as an asymmetrical south facing half‐graben, about 40 km wide, dominated by a large boundary fault zone to the north. It is partially filled up by the 1–3 Myr old Gulf Basalts which onlapped the older Somali Basalts along its shallower southern flexural margin. The major and trace element analysis of 78 young onshore lavas allows us to distinguish and map four distinct basaltic types, namely the Gulf, Somali, Goumarre, and Hayyabley Basalts. These results, together with radiometric age data, lead us to propose a revised volcano‐stratigraphic sketch of the two exposed Tadjoura rift margins and to discriminate and date several distinct fault networks of this oblique rift. Morphological and statistical analyses of onshore extensional fault populations show marked changes in structural styles along‐strike, in a direction parallel to the rift axis. These major fault disturbances are assigned to the arrest of axial fault tip propagation against preexisting discontinuities in the NS‐oriented Arta transverse zone. According to our model, the sinistral jump of rifting into the Asal‐Ghoubbet rift segment results from structural inheritance, in contrast with the en échelon or transform mechanism of propagation that prevailed along the entire length of the Gulf of Aden extensional system.