WASHINGTON—The Trump administration reached agreements with Canada and Mexico to end U.S.-imposed tariffs on steel and aluminum imports and unwind retaliatory measures, removing a major barrier to the three countries’ new trade pact.

Mr. Trump hailed the deal in a speech in Washington, saying the U.S. “just reached an agreement with Canada and Mexico and we will be selling our product into those countries without the imposition of tariffs or major tariffs.”

The...