During the Geophysical Measurements Across the Continental Margin of Namibia (MAMBA) experiments, offshore and onshore refraction and reflection seismic as well as magnetic data were collected. Together with the existing free‐air gravity data, these were used to derive two crustal sections across the ocean‐continent transition. The results show that the Early Cretaceous continental breakup and the separation of South Africa and South America were accompanied by excessive igneous activity offshore. Off Namibia we found a 150–200 km wide zone of igneous crust up to 25 km thick. The upper part of this zone consists of an extrusive section comprising three units of basaltic composition: two distinct wedges of seaward dipping reflectors (SDRs) separated by flat‐lying volcanic flows. The inner wedge of SDRs can be modeled as the source of a long‐wavelength magnetic anomaly that borders long parts of both South Atlantic margins (anomaly G). The crust underneath these extrusives is characterized by high‐velocity and high‐density material (average values 7 km s−1, 3×103 kg m−3). Free‐air gravity anomalies along both sides of the high‐density crust are interpreted as edge effects resulting from juxtaposition with normal oceanic and continental crust on either side. We define the abrupt landward termination of this zone as the continent‐ocean boundary, and consequently, the crust seaward is interpreted as exclusively igneous material and not intruded continental crust. Extrapolation of the interpreted geophysical features along the southwest African margin suggests a fast prograding narrow rift zone and sharp lithospheric rupture leading to the formation of a margin‐parallel magmatic belt south of the Walvis Ridge. The influence of the Tristan da Cunha mantle plume may explain the widening of this thick igneous crust near the Walvis Ridge.