Anthropogenic fluid injections are known to induce earthquakes. The mechanisms involved are poorly understood, and our ability to assess the seismic hazard associated with geothermal energy or unconventional hydrocarbon production remains limited. We directly measure fault slip and seismicity induced by fluid injection into a natural fault. We observe highly dilatant and slow [similar to 4 micrometers per second (mm/s)] aseismic slip associated with a 20-fold increase of permeability, which transitions to faster slip (similar to 10 mu m/s) associated with reduced dilatancy and micro-earthquakes. Most aseismic slip occurs within the fluid-pressurized zone and obeys a rate-strengthening friction law mu = 0.67 +/- 0.045ln (v/v(0)) with v(0) = 0.1 mu m/s. Fluid injection primarily triggers aseismic slip in this experiment, with micro-earthquakes being an indirect effect mediated by aseismic creep.