WASHINGTON — The administration and House Democrats have reached an agreement in principle to modify President Trump’s revised North American trade pact, removing one of the last hurdles to enacting the president’s signature trade deal.

The agreement, announced Tuesday by Speaker Nancy Pelosi, comes at an odd moment as the same group of House Democrats moved closer toward impeaching the president. Ms. Pelosi of California said she would allow the deal to move forward in the House, handing the administration one of its biggest legislative victories less than an hour after she announced the articles of impeachment against Mr. Trump.

The decision to proceed with the United States-Mexico-Canada-Agreement came after Democrats said they secured additional labor, pharmaceutical, environmental and enforcement provisions in a trade pact that governs commerce across North America. Those changes were critical to winning the support of labor unions, including the powerful AFL-CIO.

The changes to USMCA, which the three countries signed more than a year ago, must now be woven into implementing legislation that the House and Senate will both vote on. The pact will also need to secure the president’s signature and the final approval of the Mexican senate and Canadian leadership.

At a news conference on Tuesday, Ms. Pelosi, flanked by Democrats including Massachusetts Representative Richard E. Neal, said that they were confident that the legislation would become law, replacing the much-maligned North American Free Trade Agreement and fulfilling a legislative priority for both the administration and the House Democratic caucus.

“It is infinitely better than what was initially proposed by the administration,” Ms. Pelosi said. “It’s a victory for America’s workers.”

“This is a transformative agreement,” Mr. Neal said.

Mr. Trump, who has spent weeks blaming Ms. Pelosi for obstructing completion of a trade deal that he says will help workers, touted the progress on Twitter earlier on Tuesday morning. “Looking like very good Democrat support for USMCA. That would be great for our Country!”

The timing of the handshake agreement offers Mr. Trump a crucial victory to tout on the campaign trail during his re-election bid and House Democrats tangible proof that they are able to legislate while preparing to vote on charges of abuse of power and obstruction of Congress against the president. While it is unclear when legislation will be ready for the House floor, it could come as lawmakers are readying for a vote on impeachment articles.

“We’re going to begin to share text and review parts of the agreement before there’s an expedited period of bringing it to the floor” Mr. Neal said. “There’s no reason for unnecessary delays.”

Given the ongoing impeachment inquiry and Democratic opposition to both Mr. Trump and NAFTA, the House majority is offering a remarkable trade win to the administration.

But the closed door negotiations between a select group of Democrats and Mr. Lighthizer gave them an opportunity to secure multiple policy changes related to prescription drug pricing, the environment, labor protections and dispute settlement.

That included removing a provision that Democrats criticized as a boon to the pharmaceutical industry. Democrats had objected to provisions governing intellectual property protections for new pharmaceutical products, in particular an advanced class of drugs called biologics, which were given 10 years of protection from cheaper alternatives. Congressional Democrats said those measures could undermine efforts to make American health care more affordable and the revised deal strips out that 10 year protection.

Democrats have also been eager to lock in provisions that they see as improvements on the original NAFTA, and provide more certainty to the businesses in their districts that depend on the pact.

The administration and Republicans in both chambers have hammered Ms. Pelosi and her caucus for weeks over the delay in allowing the pact’s legislation to go for a vote on the House floor. Even within Ms. Pelosi’s majority, several moderate members and a number of the freshmen responsible for flipping seats and delivering her the majority had begun pressuring leadership for a vote on the pact before the end of the year.

The deal announced Tuesday offered Ms. Pelosi and her core allies justification for the delay by establishing what she said would be a legacy agreement that sets the standard for future trade deals.

The rewrite provides a much-needed update to the trading rules for North America. The original NAFTA, which was negotiated by President George H.W. Bush and signed by President Clinton, went into force on January 1994, before the commercialization of the internet.

Besides updating rules for digital commerce, Mr. Trump’s USMCA has made other changes generally sought by Democrats, like raising the threshold for the proportion of a car’s value that must be made in North America in order to qualify for the pact’s zero tariffs. It also contains provisions designed to strengthen Mexican labor unions and roll back a special system of arbitration for corporations long opposed by Democrats.

With passage into law in the United States, the deal will clear its biggest and one of its last remaining hurdles in a tumultuous two-year negotiation.

Since beginning the negotiations in August 2017, Mr. Trump peppered the talks with accusations that Canada and Mexico were ripping off the United States, as well as frequent threats to withdraw from the pact altogether. He and his advisers pressed for concessions that were opposed by both foreign officials and the business community, including a sunset provision that could have caused the pact to automatically expire.

The Trump administration ultimately watered down some of its more controversial demands and secured the approval of Canada and Mexico late last year. Mexico’s legislature has already ratified the agreement, and in Canada the trade pact is expected to pass into law without controversy.

Elisabeth Malkin contributed reporting from Mexico City.