Valverde, 35, posted a 5.59 ERA and had nine saves in 12 attempts with the Detroit Tigers last season before ultimately getting released from Triple-A Toledo on Aug. 7.
Valverde went 49-for-49 in save attempts for Detroit in 2011. But the following year he struggled during the playoffs and became a free agent. The Tigers eventually re-signed him to a minor league deal for last season and promoted him in mid-April.
The Mets have brought in Valverde and Kyle Farnsworth on minor league deals as protection with closer Bobby Parnell attempting to return from neck surgery. Set-up man LaTroy Hawkins departed in free agency to the Colorado Rockies.
Parnell has indicated he feels fine, but he is first due to throw off a mound in two weeks. He underwent surgery Sept. 10 to repair the herniated disk.