The three minor leaguers that were sent to Detroit were left-handed pitchers Matt Boyd, Jairo Labourt, and Daniel Norris, who will start on Sunday for the Tigers.
Price is 9-4 this season with a 2.53 ERA, and is coming off a rough outing at Tampa Bay in front of numerous scouts. The left-hander will be a free agent after the season.
The Blue Jays made their second big move of the week, after acquiring Troy Tulowitzki from the Colorado Rockies on Tuesday. They look to make a push in the AL East, as they sit six games behind the New York Yankees in the division.
Toronto currently has the longest postseason drought in baseball, not making it to October since 1993.
Their new ace is a career 7-0 with a 3.86 ERA at the Rogers Centre, which is his most wins without a loss at any stadium. Toronto's odds to win the World Series moved from 25-1 to 16-1, according to Westgate SuperBook. The Kansas City Royals are the favorites at 7-2 odds.
It is the second consecutive year that Price was moved around the trade deadline, as the Tigers picked him up in a three-team deal from the Tampa Bay Rays at last year's deadline.
Detroit has struggled, despite sitting just three and a half games behind the Minnesota Twins in the wild card race. They are 50-52, 11 1/2 games behind the Royals, after starting the season 11-2.
They continued to sell on Thursday when they sent closer Soria to the Pittsburgh Pirates for a minor league infielder.
Price, the 2012 AL Cy Young Award winner, joins the likes of Mark Buehrle and R.A. Dickey in a rotation that is supported by one of the best lineups in the game. The Blue Jays are just two games out of a playoff spot, and now have more than enough on their roster to make a deep playoff push.