The agreements will bring to 20 those countries that have free-trade relations with the United States.
Trade won't go away as an issue, as the administration pushes ahead with a major Pacific Rim trade pact, Congress and the White House scuffle over China, and Republicans take aim at Obama's policies during the presidential campaign.
But, "I don't see this administration coming up with new free trade agreements," said National Foreign Trade Council president Bill Reinsch. "For the next six months we ought to go after trade liberalization in manageable pieces."
Republicans accuse the administration of moving too slowly to find new free-trade partners, resulting in U.S. exporters losing out to foreign rivals. The administration says it is promoting free trade, but wants to assure that the other side is playing by the rules, that basic worker and environmental rights are observed, and that deals promote U.S. job growth.
"From day one," U.S. Trade Representative Ron Kirk said, the guiding principle has been not just to complete the three trade agreements but "to develop a new paradigm for trade, and rebuild and restore America's confidence in our trading policy."
He added that the administration was on track to reach Obama's goal, set early last year, of doubling U.S. exports over a five-year period.
Trade officials, in justifying their approach, point to the 83 Senate votes for the South Korean deal, which was renegotiated by Obama to expand access for U.S. vehicles in Korea. That was the highest total ever for a free-trade vote.
Obama also signed legislation extending a program, a Democratic favorite, to help workers hurt by foreign trade. Yet the quiet signing ceremony and a low-key reception in the Rose Garden for those who might benefit from the agreements reflected the unpopularity of free-trade pacts among Obama's core labor supporters - and the uncertainty of his future trade policy.
After the signing, Obama called Presidents Juan Manuel Santos of Colombia and Ricardo Martinelli of Panama to congratulate them.