According to a Major League source, Damon will be paid $5.25 million with a $750,000 attendance bonus, while Ramirez will make $2 million.
The Rays have not confirmed the deals, nor have they commented on either player.
For the length of the offseason, Rays fans have sat by patiently waiting for the team to reveal its hand for the 2011 season. After losing first baseman Carlos Pena and left fielder Carl Crawford to free agency, the Rays needed to address their run production for the coming season.
This latest news should adequately insure the Rays will not lack any firepower in 2011.
Damon, 37, manned left field and served as designated hitter for the Tigers last season, hitting .271 with eight home runs and 51 RBIs, and he scored 81 runs over 145 games. He has played for two World Series champions -- the Red Sox in 2004 and the Yankees in 2009.
With 2,571 career hits, Damon stands just 429 from the 3,000 mark. He will likely serve time in left field, at DH and come off the bench for the Rays, and he adds a quality veteran presence to the clubhouse.
Ramirez, 38, hit .311 with eight home runs and 40 RBIs in 66 games for the Dodgers in 2010 before finishing the season with the White Sox, where he batted .261 with one home run and two RBIs in 24 games. He has 555 career home runs -- 14th on the all-time leaderboard -- and is a 12-time All-Star.
Ramirez was suspended 50 games in 2009 for violating Major League Baseball's Performance Enhancing Drug policy for taking human chorionic gonadotropin (hCG), a women's fertility drug typically used by steroid users to restart the body's natural testosterone production as they come off a steroid cycle.
Ramirez will likely be used primarily as a DH and will give Evan Longoria protection in the Rays' lineup.
Damon and Ramirez were teammates in Boston from 2002-05 and were key members of the club's World Series championship in 2004.
The Angels and Rangers were also suitors for Ramirez.