WASHINGTON—The Senate confirmed Robert Lighthizer to serve as U.S. trade representative, paving the way for the Trump administration to launch a renegotiation of the North American Free Trade Agreement and accelerate more broadly plans to reorient American trade policy.

While most of President Donald Trump’s nominees have cleared a divided Congress by narrow margins with mainly Republican support, Mr. Lighthizer on Thursday won significant backing from Democrats as well. That is a sign that, even as the opposition party battles...