The deal includes an additional $500,000 per year in incentives based on games finished, a source told ESPN.com's Jerry Crasnick.
Rodney reported to spring training on Wednesday and passed his physical, clearing the way for the Mariners to make his signing official. He took part in Thursday's first workout for pitchers and catchers.
Rodney, 36, was 5-4 with 37 saves and a 3.38 ERA for the Tampa Bay Rays in 2013. He ranked second in the American League in saves and ERA over the past two seasons, with a combined 85 saves and a 1.91 ERA.
He made the AL All-Star team and finished fifth in Cy Young Award balloting in 2012.
The Associated Press contributed to this report.