Price acknowledged the deal Thursday on his official Twitter account, sending out his thanks to Tampa Bay fans.
wow...what a day!! Rays fans THANK YOU!! Great Chapter of my life just ended...ready to start a new one with the Tigers!! Thanks again- David Price (@DAVIDprice14) July 31, 2014
The Rays also received infield prospect Willy Adames from the Tigers.
"The question that we asked ourselves is: What gives us the best chance of winning the world championship this year?" Tigers general manager Dave Dombrowski said. "We thought adding him to our rotation at this point would give us the best chance to do that.
"Today it's great, it's nice, it's fine. I love to have David Price. If we win, then I'll be very satisfied."
The Rays said the trade was in the best interests of the franchise.
"Compared to the other possibilities, it was by far the most prudent thing that we could do," said Andrew Friedman, Tampa Bay's vice president of baseball operations. "If you look ahead to next year, it would have been really challenging to be as good as we want to be within our situation, with David taking up that meaningful of a percentage of our payroll. So everything we do is in the vein of how to be competitive in the near term and also the long term."
The Rays also aren't giving up on this season.
"It's not waving a white flag at all," Rays president Matt Silverman said. "If your team plays to the level that it can, especially considering all the head-to-head games we have within our division, we have a chance to make up the deficit and get into the playoffs. It's more difficult without David, but if the rest of the team plays up to their potential, we're going to be playing meaningful games in September."
Rays manager Joe Maddon addressed the trade on Twitter, writing:
No fun losing a David Price. Hate it. But we have to do what is best for our group. Continue to move it forward and that's what we've done.- Joe Maddon (@RaysJoeMaddon) July 31, 2014
The deal was completed just ahead of Thursday's 4 p.m. ET deadline for non-waiver trades.
Jackson was pulled from Detroit's game Thursday afternoon against the Chicago White Sox with one out in the top of the seventh and was seen hugging several teammates before exiting into the clubhouse.
"It's kind of a weird moment right there taking that last jog off the field knowing that's pretty much the last time I will be running off in a Tigers uniform," said Jackson, who is hitting .273 and has been Detroit's regular center fielder throughout its recent run of division titles.
"I really didn't know what to do because I've never been in that situation where you're taken out of a game in the middle of an inning. I knew what was going on, I was just in a daze a little bit and was trying to let everything play out."