Also agreeing to Minor League deals are outfielder Cole Gillespie and right-handed pitcher Matt Palmer.
The three are not on the Mariners' 40-man roster, which is currently full, but they will take part in Major League camp in Peoria, Ariz., which opens with pitchers and catchers reporting on Feb. 12.
Ramirez is the most experienced of the group, having pitched with the Rockies (2006-07), Royals ('08), Red Sox (2009-10), Giants (2010-11 and '13) and Mets ('12).
The Dominican native was a key member of the Giants' World Series championship club in 2010 as he put up a 0.67 ERA with just two earned runs allowed in 27 innings in 25 relief appearances over the final two months of the year.
Ramirez pitched six games for the Giants last year, posting an 11.12 ERA with nine hits, seven earned runs, five walks and no strikeouts in 5 2/3 innings before his release. But he went 3-1 with a 3.31 ERA in 27 appearances in the Minors and has thrown well in winter ball in the Dominican this offseason, with a 3.15 ERA in 21 relief outings for Gigantes del Cibao.
In his career, Ramirez is 23-21 with a 3.42 ERA in 423 relief appearances since signing with the Rangers initially as an outfield prospect in 1996.
Palmer, 34, is a veteran right-hander who pitched for the Dodgers' Triple-A Albuquerque club last year and went 6-8 with a 3.84 ERA in 25 games, including 22 starts. Palmer last pitched in the Majors in 2012 with three relief appearances for the Padres.
The 6-foot-2, 235-pounder was a fifth starter and long reliever in 2009 with the Angels and went 11-2 with a 3.93 ERA in 121 1/3 innings in 40 games, including 13 starts. But he's pitched only 20 games in the Majors since and has a career MLB mark of 13-7 with a 4.56 ERA.
Gillespie, 29, is a former Oregon State standout and Portland, Ore., native, who hit .240 (12-for-50) in 25 games last year with the Cubs after being released by the Giants in July. He has played all three outfield positions in parts of three seasons with the D-backs (2010-11), Giants ('13) and Cubs ('13).
Gillespie has batted .225 with three home runs and 20 RBIs in 78 career games since being selected in the third round of the 2006 Draft by the Brewers.
Like all clubs, the Mariners sign a number of players to Minor League deals with camp invites to add depth and competition in Spring Training and typically a couple land jobs on the Major League roster at some point during the season.
Seattle will likely add a few more veterans to that list, as well as extending Spring Training invitations to some of their own top Minor League players, between now and the start of camp.