We study deep aseismic slip along the central section of the San Jacinto Fault, near the Anza Seismic Gap, in southern California. Elevated strain rates following the remote Mw7.2, 4 April 2010 El Mayor‐Cucapah and the local Mw5.4, 7 July 2010 Collins Valley earthquakes were recorded by Plate Boundary Observatory borehole strainmeters near Anza and were accompanied by vigorous aftershock sequences. We introduce a method to infer the distribution of triggered aseismic slip from combined seismicity and geodetic data, based on a rate‐and‐state friction model that maps observed changes in seismicity rates into stress changes. We invert for the cumulative slip in the 10 day period following each main shock. Synthetic tests show that the effect of aftershock interactions on the inferred slip distribution is negligible. The joint data set is more consistent with a model in which aseismic slip on a principal fault triggers seismicity on adjacent faults than with one in which aseismic slip and seismicity are coplanar. Our results indicate that aseismic slip primarily occurs along the rim of two seismicity clusters adjacent to Anza Gap, as well as beneath the Anza Gap itself, at depths larger than 10 km. The triggered aseismic slip generated by the two main shocks has little overlap, a pattern also found in sequences of large earthquakes occurring on a same fault. Stresses inferred from seismic activity leading to the Collins Valley main shock suggest that this earthquake was triggered by stresses imposed by the El Mayor‐Cucapah remote‐triggered aseismic slip, which persisted for more than 2 months.