Damon agreed to a one-year deal worth $5.25 million plus incentives and Ramirez one year at $2 million, according to SI.com. Both deals are pending physicals. Damon will likely play left field and Ramirez designated hitter.

The moves mark the first major additions for the AL East champions after a devastating offseason in which one prominent player after another left cost-conscious Tampa Bay.

Carl Crawford, Carlos Pena and Rafael Soriano signed elsewhere as free agents. Matt Garza and Jason Bartlett were traded. A strong bullpen was depleted by the losses of Joaquin Benoit, Dan Wheeler and Chad Qualls.

Ramirez and Damon played together for years in Boston and helped lead the Red Sox to the 2004 World Series title. Both colorful characters are past their prime, but if nothing else they could at least provide an attraction at Tropicana Field for a Rays team that drew just 1.86 million fans last year.

The 37-year-old Damon hit .271 with eight home runs and 51 RBIs with the Detroit Tigers last season. He has 2,571 career hits in 16 seasons with Kansas City, Oakland, Boston, New York and Detroit.

Ramirez, 38, hit .298 with nine home runs and 42 RBIs last season with the Los Angeles Dodgers and Chicago White Sox. He was limited to 265 at-bats in 2010 because of problems with his right knee and left groin. The latter led to hernia surgery in October.

In 18 major league seasons, Ramirez has a .313 average with 555 home runs and 1,830 RBIs. The 12-time All-Star believes he can extend his career a bit longer as a DH.

Information from ESPN.com senior writer Jerry Crasnick, ESPNdeportes.com's Enrique Rojas and The Associated Press was used in this report.