WASHINGTON — A House committee vote today set in motion the final act of the long drama of approving free trade agreements with South Korea, Colombia and Panama.

The Ways and Means Committee votes for the three agreements set the stage for full House approval next week and Senate votes in the near future.

The committee action came just two days after President Barack Obama submitted the deals to Congress for final approval, and reflected the desire to move swiftly on trade deals that both the White House and most members of Congress say could mean a significant boost in U.S. exports and create tens of thousands of jobs.

That speed comes after years of delay. All three agreements were signed during the George W. Bush administration, but the Obama White House refused to send them to Congress until it renegotiated key issues, specifically on access to South Korea for U.S. automakers and Colombia’s protections for labor rights.

The White House also held up the deals until it was assured that Congress would act to extend expired provisions of a program that offers retraining and financial benefits for workers displaced by foreign competition. The Senate last week passed the worker aid bill, and the House plans to take it up next week in conjunction with the trade deals.

“For the past five years we have been working towards this day,” Ways and Means Committee Chairman Dave Camp, R-Mich., said. With the nation’s high unemployment rate, “we must look at all opportunities to create American jobs. These agreements do just that.”

All four bills are expected to pass by comfortable margins. Many Republicans are negative toward extension of the Trade Adjustment Assistance program — the worker aid bill — but say they will vote for it to assure approval of the trade deals.

Many Democrats also remain opposed to the agreement with Colombia because of its history of suppression of labor rights and violence against labor leaders.

Obama and Colombian President Juan Manual Santos in April signed a Labor Action Plan that commits Colombia to passing laws to protect labor rights, protecting labor organizers and prosecuting those accused of acts of violence against labor leaders. Democrats have welcomed that step, but say it is not enough.

“There remain troubling problems with how Colombia is addressing key elements related to the Action Plan,” said the top Democrat on the committee, Sander Levin of Michigan, who argued that the plan should have been written into the bill implementing the trade agreement.

The three countries already enjoy near duty-free status for most of the goods they sell to the United States, and the free trade deals will eliminate or significantly reduce tariffs on most U.S. agriculture and manufactured goods. The White House says that will result in some $13 billion in increased U.S. exports annually — $10 billion to South Korea alone — and foster tens of thousands of jobs.

Those figures are disputed by labor groups and other free trade opponents who contend that in the past free trade has contributed to a loss of manufacturing jobs in the United States and the flight of factories overseas.