We investigate the effects of free trade agreements (FTAs) on tariffs of non-member countries. In our multi-country model, the formation of an FTA leads members to reduce their exports to the rest of the world. Such external trade diversion weakens the ability of non-members to manipulate their terms of trade vis-a-vis FTA members, a mechanism that induces them to lower their tariffs on FTA members. We empirically confirm this insight using industry-level trade data for 192 importing and 253 exporting countries, along with information on all FTAs formed in the world during 1989-2011.