As part of the deal, the Mariners sent infielder Nick Franklin to Tampa Bay, the Rays sent Price to Detroit, and Detroit sent Jackson to Seattle and pitcher Drew Smyly to Tampa Bay, ESPN said.
Jackson, 27, is a career .277 hitter who is hitting .273 this year with 4 home runs and 32 RBIs in 99 games. He has been Detroit's regular center fielder throughout this run of division titles.
Jackson was removed from Detroit's game against the Chicago White Sox with one out in the top of the seventh inning. As he jogged in from center field, he got a nice hand from the home fans, many of whom no doubt understood the significance of the substitution moments before the trade deadline.
The 23-year-old Franklin hit .294 in 75 games this season with Triple-A Tacoma. He appeared in 17 games with the Mariners, hitting .128.
It's the second trade the Mariners made for an outfielder on the non-waiver trade deadline Thursday, earlier acquiring outfielder Chris Denorfia from the San Diego Padres for outfielder Abraham Almonte, their opening day starter in center field, and right-hander Stephen Kohlscheen. Almonte made the club out of spring training but lasted only 27 games before being optioned to the minors.