The two-time All-Star agreed to a minor league contract and reported to spring training on Tuesday.
Blalock hit .234 with 25 homers and 66 RBIs in 123 games for the Texas Rangers last year. He missed much of the previous two seasons with injuries and is a .269 career hitter with 152 homers and 535 RBIs.
Tampa Bay thinks the 29-year-old infielder could provide an additional left-handed hitting option and bolster the club's depth at first and third.
"We're excited to add Hank to the mix. He's got tremendous power and a guy we feel has a lot of upside," Rays executive vice president of baseball operations Andrew Friedman said in Sarasota, where Tampa Bay was playing an exhibition against the Baltimore Orioles.
"We're anxious to get him started and see what we've got and put him in a position to compete for a job," he said.
Blalock spent the first eight seasons of his career with the Rangers. He was an All-Star in 2003 and 2004.
"He looks like he's in great shape," Rays manager Joe Maddon said before the game.
Maddon conceded it may be difficult for Blalock to play his way onto the 25-man roster by early April, when the regular season begins.
"But things change. He could come out and do a really good job or he could look really good and all of a sudden he's going to make us think differently," the manager said. "Somebody could get hurt. Obviously that enhances his chances. All those things are possible."
Blalock's contract includes an option that would allow him to opt out and seek a job with another team if he doesn't wind up on the 25-man roster.
"I'm much more focused on the player and how it may potentially impact us," Friedman said. "But what I will say is at the end of spring if there is not a 25-man spot for him, and there is somewhere else, we're not going to stand in the way."