The passage of radiating seismic waves generates transient stresses in the Earth’s crust that can trigger slip on faults far away from the original earthquake source. The triggered fault slip is detectable in the form of earthquakes and seismic tremor. However, the significance of these triggered events remains controversial, in part because they often occur with some delay, long after the triggering stress has passed. Here we scrutinize the location and timing of tremor on the San Andreas fault between 2001 and 2010 in relation to distant earthquakes. We observe tremor on the San Andreas fault that is initiated by passing seismic waves, yet migrates along the fault at a much slower velocity than the radiating seismic waves. We suggest that the migrating tremor records triggered slow slip of the San Andreas fault as a propagating creep event. We find that the triggered tremor and fault creep can be initiated by distant earthquakes as small as magnitude 5.4 and can persist for several days after the seismic waves have passed. Our observations of prolonged tremor activity provide a clear example of the delayed dynamic triggering of seismic events. Fault creep has been shown to trigger earthquakes and we therefore suggest that the dynamic triggering of prolonged fault creep could provide a mechanism for the delayed triggering of earthquakes.