The trade sends Detroit outfielder Austin Jackson to the Seattle Mariners and Tigers left-handed pitcher Drew Smyly and Mariners infielder Nick Franklin to the Rays. The deal originally was reported by FOX Sports senior baseball writer Ken Rosenthal and has been announced by the Tigers.
The Rays also receive minor-league shortstop Willy Adames from Detroit.
Price is 11-8 with a 3.11 ERA in 23 starts this season. He leads the majors with 189 strikeouts and 170 2/3 innings pitched.
Price, 28, was the first overall pick in the 2007 draft by the Rays, with whom he has spent his entire seven-season major-league career.
The 2012 AL Cy Young Award winner and four-time All-Star is under contract through the 2015 season, meaning he isn't merely a two-month rental during the playoff push. There was some debate whether the Rays would deal Price after clawing their way back into wild-card contention this month, but they ultimately chose to part ways with their No. 1 starter.
However, when Price finally was traded, it was to an unexpected bidder.
The AL Central-leading Tigers are trying for their fourth consecutive division title, and their starting rotation was already a strength. General manager Dave Dombrowski decided to trade for Price anyway, giving Detroit a collection of stars on the mound that could be tough to match in any postseason series.
''The question that we asked ourselves is: What gives us the best chance of winning the world championship this year?'' Dombrowski said. ''We thought adding him to our rotation at this point would give us the best chance to do that.''
The deal came just hours after the Oakland Athletics got an ace of their own, Jon Lester from the Boston Red Sox
Price joins Max Scherzer and Justin Verlander in the Detroit rotation, giving the Tigers the past three American League Cy Young winners.
The Tigers are the first team with three pitchers on the staff who have all won Cy Young Awards over the previous three seasons, according to STATS.
''Today it's great, it's nice, it's fine. I love to have David Price,'' Dombrowski said. ''If we win, then I'll be very satisfied.''
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.
Price's departure became a clear possibility when the Rays fell way behind in the AL East race earlier this season. Tampa Bay has played much better over the last month and entered Thursday only 5 1/2 games behind a wild card, but the Rays decided to deal their ace anyway.
''Compared to the other possibilities, it was by far the most prudent thing that we could do for the best interests of the franchise,'' 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.''
Tweeted Rays manager Joe Maddon: ''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.''
Tampa Bay signed Price to a $14 million deal for this season, avoiding arbitration, but he isn't eligible for free agency until after next season. That means Detroit's rotation, which also includes Anibal Sanchez and Rick Porcello, should be impressive in 2015 even if Scherzer leaves via free agency this offseason.
''We're trying to win this year, but we do have David Price for next year,'' Dombrowski said. ''That's helpful.''
The Tigers are without a World Series championship since 1984. Last season's team lost to Boston in the AL championship series.
''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.''
With a lineup anchored by Miguel Cabrera, Victor Martinez and Ian Kinsler, and that remarkable rotation, Detroit has remained in first place for almost all of 2014. The Tigers tried to shore up one trouble spot, the bullpen, by trading for Joakim Soria last week.
Now Detroit has emerged with Price in another bold move aimed at bringing a championship to the Motor City.
''I don't know if we're going to win by any means — there's other good clubs,'' Dombrowski said. ''But getting the opportunity to add a guy like David Price doesn't come along very often.''