The implementing legislation for the trade pact will now head to the Senate, though Senator Mitch McConnell of Kentucky, the majority leader, has said he will wait to hold a vote until the conclusion of an impeachment trial. While Republicans in the upper chamber have chafed at being left out of the final wrangling over language, the measure is expected to pass and head to Mr. Trump’s desk.

“I don’t think the Senate should just quietly agree to be jammed in this process,” said Senator John Cornyn, Republican of Texas, acknowledging that his “irritation with the process” would probably not prompt him to vote against the deal.

Mr. Lighthizer has said that his goal was to write a new kind of trade agreement that could win the support of a majority of both Democrats and Republicans. Through the last two years of negotiations, he consulted with Democrats, labor unions and progressive groups to find common ground between their priorities and those of the Trump administration, as well as Canada and Mexico.

But Democrats would not support the agreement until they had secured critical changes to labor, environmental and enforcement provisions. And after regaining the majority in January, House Democrats knew they had substantial leverage.

Senator Sherrod Brown of Ohio, who has not supported a trade agreement in 25 years but will vote for the U.S.M.C.A., said Democrats were able to win strict labor standards by holding out their support until the Trump administration agreed in recent weeks to include them. He cast that as a victory for unions and for workers.

“The importance to this is that workers are not just at the table, but have real power,” Mr. Brown said, “which has never happened before in a trade deal.”

House Republicans, who have hammered their Democratic counterparts for not immediately rushing the agreement text to the floor after it was signed more than a year ago, mostly celebrated the agreement in speeches on the House floor.