Lyon spent last season with Houston and Toronto, going a combined 4-2 with a 3.10 ERA and one save. He had 63 strikeouts in 61 innings spanning 67 appearances.
The 33-year-old right-hander has 79 career saves and a 4.12 ERA in 11 major-league seasons. He saved 26 games for Arizona in 2008 and 20 for Houston in 2010.
Lyon can earn an additional $1.65 million in performance bonuses. The only other free agent to receive a major-league contract from the Mets this offseason was pitcher Shaun Marcum, who got a $4 million, one-year deal to replace NL Cy Young Award winner R.A. Dickey in the rotation.
Dickey was traded to Toronto for prospects.
Marcum can make another $2.25 million in performance bonuses and $1.75 million in roster bonuses.
Francisco had surgery in December to remove a bone spur from his right elbow. The Mets said then that he was expected to be ready for opening day. The right-hander struggled last year in an injury-plagued first season with the Mets, going 1-3 with a 5.53 ERA and 23 saves in 26 chances.
Even if Francisco holds onto his job as closer, Lyon figures to fill a late-inning role in New York's revamped bullpen.
The Mets have been trying to make over a group of relievers that was one of the worst in the majors last season. General manager Sandy Alderson has signed veterans LaTroy Hawkins, Scott Atchison and Pedro Feliciano to minor-league contracts with invitations to spring training.