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Studies that attempt to simulate continental rifting and subsequent breakup require detailed knowledge of crustal stresses, however observational constraints from continental rifts are lacking. In addition, a knowledge of the stress field around active volcanoes can be used to detect sub-surface changes to the volcanic system. Here we use shear wave splitting to measure the seismic anisotropy of the crust in Northern Afar, a region of active, magma-rich continental breakup. We combine shear wave splitting tomography with modelling of gravitational and magmatic induced stresses to propose a model for crustal stress and strain across the rift. Results show that at the Ethiopian Plateau, seismic anisotropy is consistently oriented N–S. Seismic anisotropy within the rift is generally oriented NNW–SSE, with the exception of regions north and south of the Danakil Depression where seismic anisotropy is rift-perpendicular. These results suggest that the crust at the rift axis is characterized by rift-aligned structures and melt inclusions, consistent with a focusing of tectonic extension at the rift axis. In contrast, we show that at regions within the rift where extension rate is minimal the seismic anisotropy is best explained by the gravitationally induced stress field originating from variations in crustal thickness. Seismic anisotropy away from the rift is controlled by a combination of inherited crustal structures and gravitationally induced extension whereas at the Dabbahu region we show that the stress field changes orientation in response to magmatic intrusions. Our proposed model provides a benchmark of crustal stress in Northern Afar which will aid the monitoring of volcanic hazard. In addition we show that gravitational forces play a key role in measurements of seismic anisotropy, and must be considered in future studies. We demonstrate that during the final stages of continental rifting the stress field at the rift axis is primarily controlled by tectonic extension, but that gravitational forces and magmatic intrusions can play a key role in the orientation of the stress field.