Seattle has two returning relievers -- right-handers Danny Farquhar and Tom Wilhelmsen -- who combined to save 40 games last season, though both had ERAs above 4.00 for the season.
Rodney's agreement was initially reported by Grantland, which said the veteran right-hander could earn up to $15 million over the two seasons if he meets incentives.
Any deal with Rodney won't be official until he passes a physical, which will likely come next week. Mariners pitchers and catchers report to Spring Training on Tuesday in Peoria, Ariz.
After nine years with the Tigers and Angels, Rodney had a breakout year with the Rays in 2012, when he racked up 48 saves with a 0.60 ERA, striking out 76 batters in 74 2/3 innings to earn his first All-Star Game berth, the American League Comeback Player of the Year Award and a fifth-place finish in the AL Cy Young Award voting.
He was not as overpowering last season, but still recorded 37 saves and a 3.38 ERA with 82 strikeouts in 66 2/3 frames.
For his career, the Dominican native has a 3.70 ERA and 172 saves with 551 strikeouts in 571 1/3 innings.
Rodney earned $2.5 million last year with the Rays and was regarded as one of the premier relievers on this year's free-agent market.
Wilhelmsen, 30, began last year as the Mariners' closer after taking over the role from Brandon League midway through 2012 and saving 29 games with a 2.50 ERA in 73 appearances.
He got off to an outstanding start again last year, racking up 12 saves with a 0.75 ERA in the first two months before running into control issues and eventually being sent to Triple-A Tacoma. Wilhelmsen finished last year with a 4.12 ERA, 45 strikeouts and 33 walks in 59 innings after striking out 87 and walking 29 in 79 1/3 frames in 2012.
Farquhar, 26, replaced Wilhelmsen in the closer's role for the final two months and finished with 16 saves, tied for the third most in the Majors behind only Greg Holland of the Royals (19) and Craig Kimbrel of the Braves (18) while in that role from Aug. 3 to the end of the season.
While Farquhar finished 0-3 with a 4.20 ERA in 46 appearances, his ERA was 1.69 over his final 29 outings and his season average of 12.77 strikeouts per nine innings ranked fourth among all AL relievers.
Rodney's addition would seemingly allow Wilhelmsen and Farquhar to compete for right-handed setup roles along with Yoervis Medina, which would solidify that situation after the trade of Carter Capps to the Marlins for Logan Morrison. Stephen Pryor, another hard-throwing right-hander, isn't expected back until midseason as he comes off shoulder surgery.
The Mariners have Charlie Furbush and Lucas Luetge returning as left-handed relievers.