Toronto also acquired catchers Josh Thole and Mike Nickeas from the New York Mets in exchange for catchers John Buck and Travis d'Arnaud, minor-league right-hander Noah Syndergaard and minor-league outfielder Wuilmer Beccera.
Dickey proclaimed on Twitter: "Looking forward to a new chapter with the Jays."
He went on to express his gratitude to Mets fans for their support.
The Jays were granted a 72-hour negotiation window with Dickey’s representative that was to expire at 2 p.m. ET on Tuesday.
The 38-year-old right-hander is signed for $5 million US next season. The Jays agreed to an extension worth $24 million for the two subsequent seasons, with a club option for $12 million in 2016.
Thole hit .234 in 104 games with New York last season, with one home run and 21 runs batted in. The 26-year-old Breese, Ill., native has a .261 career average in 916 plate appearances at the major-league level, all with the Mets.
Vancouver native Nickeas, 28, has spent most of his career in the minors, batting just .180 in 172 at bats in the majors.
The 23-year-old d'Arnaud was viewed as the Jays' No. 1 prospect after earning MVP honours with double-A New Hampshire in the Eastern League, while the 20-year-old Syndergaard was also ranked highly. The 6-foot-5 Syndergaard struck out 122 in 19 games at class-A Lansing.
Buck, 32, was acquired in Toronto's multi-player deal last month with the Miami Marlins, but won't suit up for a second tenure with the Jays. He played for Toronto in 2010, part of a major-league career that has seen him hit 118 home runs with 423 runs batted in over 948 career games.
Mets general manager Sandy Alderson put his best spin on the deal from New York's perspective.
"We feel that players acquired in this deal, Buck and d'Arnaud in particular, will make contributions in 2013," Alderson said.
Dickey was named the top pitcher in the NL in 2012 after posting a 20-6 record and 2.73 earned-run average for the Mets.
He is coming off a season in which he led the NL in strikeouts (230), ERA, innings (233 2/3), complete games (five) and shutouts (three).
Despite battling an abdominal injury, Dickey became the Mets' first 20-game winner since Frank Viola in 1990 and the first major leaguer in 24 years to throw consecutive one-hitters.
Spring training cut
Dickey was cut by the Mets in spring training in 2011, but worked his way to New York and earned a spot in the rotation by the end of the season.
Dickey languished in the minors for 14 years, bouncing from one team to another before finally perfecting the perplexing knuckleball that's made him a star.
He joined Dwight Gooden (1985) and three-time winner Tom Seaver as the only Mets to win the Cy Young Award.
The Los Angeles Angels and Texas also had been interested in Dickey.
Dickey drew attention earlier this month when he showed up at the baseball winter meetings in Nashville — he lives in Tennessee near the hotel where the gathering was held.
Last week, Dickey ruffled Mets management when he spoke about his contract situation during a team event at Citi Field for children displaced from their schools by Superstorm Sandy.
Dickey said it "would be disappointing" if he merely played out his option year 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 at the event. "And that would be sad."
The Blue Jays have missed the playoffs since winning their second straight World Series in 1993 and have boldly moved to reshape a team that went 73-89 last season in the rugged American League 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 Marlins.
Toronto then signed free-agent outfielder Melky Cabrera, an all-star with San Francisco whose season ended when he was suspended 50 games for a positive testosterone test.
Dickey is set to become part of a stellar rotation that includes Johnson, Buehrle and returning starters Ricky Romero and Brandon Morrow.
Thole would give the Blue Jays a catcher who is familiar with handling Dickey's knuckleball. He'd join a lineup that features former home run champ Jose Bautista and Edwin Encarnacion, who hit 42 homers last season.