"Now that its official, I want to say that I don't have the words to express how grateful I am to you for the steadfast support," Dickey posted on Twitter. "Thank you for making me feel wanted."
"Looking forward to a new chapter with the Jays," he wrote.
Toronto acquired the 38-year-old knuckleballer and catchers Josh Thole and Mike Nickeas. The Mets got top catching prospect Travis d'Arnaud and catcher John Buck, plus minor league right-hander Noah Syndergaard and outfielder Wuilmer Becerra.
Earlier in the day, Dickey and the busy Blue Jays agreed to a new contract, clearing the way for the Mets to send him to a team that's spending a lot of money trying to join baseball's elite.
Dickey was already signed for $5.25 million next year. The Mets began to look at trade possibilities for the 20-game winner when the sides couldn't agree to extend his deal for two more seasons.
Toronto said his contract from 2013-15 was worth $29 million and had a club option for 2016 at $12 million. Dickey needed to pass a physical before the teams announced the deal.
The Blue Jays have missed the playoffs since winning their second straight World Series crown in 1993, and have boldly moved to reshape a team that went 73-89 last season in the rugged AL East.
Last month, they acquired a high-priced trio of All-Stars - pitchers Josh Johnson and Mark Buehrle and former Mets shortstop Jose Reyes - in a 12-player trade with the Miami Marlins.
Toronto then signed free agent outfielder Melky Cabrera, an All-Star outfielder with San Francisco whose season ended when he was suspended 50 games for a positive testosterone test.
Dickey was 20-6 with a 2.73 ERA last season, capping his rapid rise from the majors' scrap heap to an ace pitcher. He did it by perfecting a way to throw his floater faster than previous knuckleballers, and tossing it with exceptional control.
Dickey becomes part of a stellar rotation that includes Johnson, Buehrle and returning starters Ricky Romero and Brandon Morrow.
Thole gives the Blue Jays a catcher who is familiar with handling Dickey's knuckleball. He joined a lineup that features former home run champ Jose Bautista and Edwin Encarnacion, who hit 42 homers last season.
D'Arnaud turns 24 in February. He hit .333 at Triple-A Las Vegas with 16 homers and 52 RBIs before tearing a knee ligament trying to break up a double play in June. He has been an All-Star at several levels during his climb through the minors.
The Los Angeles Angels and Texas also had been interested in Dickey before the Blue Jays swooped in.
Popular with Mets fans, Dickey perturbed team management when he spoke about his contract situation last week during a club event at Citi Field for children displaced from their schools by Superstorm Sandy.
Dickey said he enjoyed playing for the Mets and added it would be "disappointing" if he went through his option year without a new deal and became a free agent.
"If that's the decision that they make, I feel like it would be unfortunate because it probably is going mean that I'm not going to be back," Dickey said then. "And that would be sad."
Buck was an All-Star with Toronto in 2010. The 32-year-old hit .192 with 12 home runs and 41 RBIs for Miami last season, then was part of the big trade between Marlins and Blue Jays.
The 20-year-old Syndergaard went 8-5 with a 2.60 ERA for Class A Lansing. The 18-year-old Becerra hit .250 with four RBIs in 11 games in the rookie Gulf Coast League.
Thole hit .234 with one homer and 21 RBIs in 104 games last season. The 26-year-old played four seasons with the Mets.
Nickeas split last season with the Mets and Triple-A Buffalo. The 29-year-old hit .174 with one homer and 13 RBIs for New York.