The pacts, signed under former president George W. Bush, are expected to boost US exports by $13 billion and benefit US agriculture and manufacturing, and will form part of Obama's plan to cut 9.1 percent unemployment.
"These agreements will support tens of thousands of jobs across the country for workers making products stamped with three proud words: Made in America," Obama said in a statement.
The move, instantly applauded by Obama's Republican foes and the US business community, came after a nearly three-year feud fed by market-access and labor worries and a fight over aid to US workers displaced by overseas competition.
There were immediate signs that the pacts could provide a rare moment of bipartisanship in deeply divided Washington.
"They will be a top priority for the House," Republican House Speaker John Boehner said, but took a swipe at Obama's years-long delay in submitting them to Congress saying it "was unacceptably long and likely cost jobs."
The office of House Majority Leader Eric Cantor said the chamber would likely approve the deals next week, before the Senate acts.
The latest snag to winning congressional support for the deals came in a dispute over Trade Adjustment Assistance (TAA), a program to compensate workers who lose jobs to overseas competition.