In the deal, the Tigers get Price, the Mariners get Tigers outfielder Austin Jackson and the Rays get left-handed pitcher Drew Smyly from the Tigers and infielder Nick Franklin from the Mariners.
Price, 28, a four-time All-Star, won the AL Cy Young award in 2012 and is 11-8 with a 3.11 ERA this season. He is eligible for salary arbitration after this season and is currently being paid $14 million.
Jackson, 27, is a standout defender in center field and is hitting .270 with four homers and 32 RBIs. He is also arbitration eligible after the season and is being paid $6 million.
Smyly, 25, is in his third season and is 6-9 with a 3.77 ERA.
Franklin, 23, has spent most of the season in the minors for Seattle and is hitting .128 in 17 games with the Mariners.