The development was a signal triumph for President Trump, whose campaign last year rested in large part on his pledge to appoint another committed conservative to succeed Justice Antonin Scalia, who died in February 2016. However rocky the first months of his administration may have been, Mr. Trump now has a lasting legacy: Judge Gorsuch, 49, could serve on the court for 30 years or more.

Vice President Mike Pence presided over the final vote Friday, a show of force for the White House on a day when his tie-breaking vote as president of the Senate was not necessary.

The confirmation was also a vindication of the bare-knuckled strategy of Senate Republicans, who refused even to consider President Barack Obama’s Supreme Court pick, Judge Merrick B. Garland, saying the choice of the next justice should belong to the next president.