Terms for the three were not disclosed, though Francoeur will make $5 million in 2010, according to SI.com, which first reported his signing Tuesday morning.
"I'm thrilled to get it out of the way a month before Spring Training," Francoeur said in a statement. "Once we get to Florida, I can concentrate just on baseball. All of us have a lot to prove this season, and I can't wait to get going."
It may not be an ideal solution for the Mets and Francoeur, who was seeking a long-term deal, but it should appease both sides for now. Francoeur, 26, is not eligible to become a free agent until after the 2011 season, giving New York another two years to try to lock him up. In the meantime, it will pay $5 million for a middle-of-the-order corner outfielder, who could bat as high as fifth with Carlos Beltran on the disabled list.
Francoeur made $3.4 million last season, his first as an arbitration-eligible player.
After joining the Mets in a midseason trade with the Braves, Francoeur hit .311 with 11 home runs over the final 75 games of the 2009 season, playing many of them with a torn ligament in his left thumb. He had offseason surgery to repair the tear.
Ryan Church, the player whom the Mets traded away to acquire Francoeur, was designated for assignment by the Braves in December, later hooking on with the Pirates.
Feliciano, 33, has been the Mets' top left-handed specialist since 2006. Last year, he broke his own club record by appearing in 88 games, posting a 3.03 ERA and holding opposing hitters to a .231 average.
Green, 30, was part of the deal that sent J.J. Putz from Seattle to Flushing last winter. A right-handed specialist, Green struggled in his first season in New York, posting a 4.52 ERA and leading many to speculate that the Mets would not tender him a contract after the season.
Last week, New York also agreed to terms with right-handed pitcher John Maine, avoiding arbitration with him, as well. The team now has just one remaining arbitration-eligible player: Angel Pagan, who exchanged figures with the Mets on Tuesday. Pagan, who made $625,000 last season, is seeking $1.8 million in 2010. The Mets countered with an offer of $1.275 million.
Pagan may have an edge if the case goes to hearing, due to the fact that Beltran's injury may force him into the starting center-field role for the early part of the season.
New York does not often go to hearing with its arbitration-eligible players -- when Oliver Perez did in 2008, he became the first Mets player to have a hearing since David Cone in 1992.
Anthony DiComo is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.