We reconcile two previously discordant source models of the 1906 San Francisco earthquake and obtain a model that satisfies both triangulation and seismic data by allowing the rupture velocity to exceed the shear-wave velocity. Employing a projection method to remove the dependence on initial station positions allowed us to make use of a more stable triangulation network, including nonrepeated angle observations along the northern San Andreas fault. This strengthens the case for significant slip over the entire northern segment of the San Andreas fault from San Juan Bautista to Cape Mendocino during the 1906 earthquake. We also found that the teleseismic body-wave data can be reconciled with the geodetically derived slip model by allowing supershear rupture. This resolves a longstanding conflict between the two previous slip models (geodetic and seismic) of this earthquake. Supershear rupture has long been recognized as a theoretical possibility for strike-slip faulting, and it has been observed in several recent large strike-slip earthquakes, which raises the prospect that it might be typical for such events. Supershear rupture leads to substantially different strong ground motion, and as a result, may need to be taken into account when developing ground-motion prediction relations for large strike-slip earthquakes. Our final slip model has a seismic moment of 7.9×1020 N m, which corresponds to a moment magnitude of Mw 7.9.