President Trump dropped his threat of tariffs on billions of dollars of Mexican imports after negotiators reached a deal on measures to stem the flow of migrants pouring into the U.S. from Mexico, averting a potentially devastating trade fight for both countries.

Mr. Trump said the tariffs, which had been set to go into effect Monday, were “indefinitely suspended,” while Mexican President Andrés Manuel López Obrador said that, thanks to the support of all Mexicans, “the imposition of tariffs on Mexican products exported to...