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 off-season 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.