In recent years slow slip events (SSE) have been observed to occur at regular intervals on the deep portions of subduction zone interfaces. These are accompanied by seismic tremor that occurs over their duration. It has been observed that tremor activity shows transient modulations in response to earth tides and the passage of seismic waves from distant earthquakes. Here we show, for the first time, geodetic evidence for the triggering of an interplate SSE itself by teleseismic surface waves. This SSE, in southwest Japan, which had an equivalent magnitude Mw 5.3 and duration of 1.5 days, was triggered by the surface waves of a Mw 7.6 earthquake in Tonga. This evidence was captured by a newly deployed sensitive strainmeter network. The triggered SSE occurred on a place on the plate interface where the recurrence time for such events had almost expired, whereas other regions, at up to 90% of the recurrence time, were not triggered. This provides information for the conditions for triggering and generation of SSEs and, perhaps, for regular earthquakes.