Rodriguez was designated for assignment by the Rays last week. To make room for Rodriguez on their 40-man roster, the Pirates designated first baseman Gaby Sanchez for assignment.
The 29-year-old Rodriguez, who is eligible for salary arbitration, hit .211 in 237 at-bats and set career bests with 12 home runs and 41 RBIs for the Rays last season.
He saw time at all four infield positions and the outfield for Tampa Bay last season.
"Maybe change is what's needed for me at this point in my career," Rodriguez told the Pittsburgh Tribune-Review. "I don't think I've reached my potential yet. I know I can do more."
Pedro Alvarez is expected to make the move from third base to first base for the Pirates in 2015.