The trade was announced less than two days after the Athletics designated Plouffe for assignment. Oakland will receive either a player to be named later or cash.
Plouffe batted just .214 with seven home runs in 58 games with the A's. The eight-year veteran became expendable in Oakland once the Athletics recalled top third base prospect Matt Chapman from the minors Thursday.
Although third base has been his primary position, Plouffe also can play first base and figures to provide depth at the position for Tampa Bay.
Plouffe, who has 103 career home runs, also could bolster a Tampa Bay offense that is batting just .227 this season against left-handed pitching -- the worst average in the American League.