Rodney, 36, will reportedly earn $14 million during the life of the contract.
He's been in the majors for 11 seasons, breaking in with the Detroit Tigers in 2002. He spent seven seasons with the Tigers and two with the Los Angeles Angels before joining the Tampa Bay Rays in 2012.
Rodney is 29-44 with 172 saves in 563 appearances in his career. He had 48 saves for the Rays in 2012 and 37 more last year. His earned run average for his career is 3.70 but it was 0.60 in 76 games in 2012 and 3.38 in 68 appearances in 2013.
The Mariners also Thursday placed Franklin Gutierrez on the restricted list. Gutierrez informed the team he won't play this season due to a relapse of a gastrointestinal problem that afflicted him last season.