The rebuilding A's will receive four minor league prospects -- right-handed pitcher Gunnar Hoglund, Toronto's top pick in the 2021 amateur draft, IF Kevin Smith and left-handed pitchers Zach Logue and Kirby Snead.
Chapman, 28, is a three-time Gold Glove winner (2018, 2019 and 2021) and was an All-Star in 2019. He spent his first five seasons with Oakland, registering a .243 career batting average.
Chapman's average has dropped every season since a career-high .278 in 2018. Last season, he batted just .210, with 27 home runs and 72 RBIs, while striking out more than 200 times.
Chapman is the latest All-Star to be traded by the A's. Oakland sent right-hander Chris Bassitt to the New York Mets last week for a pair of minor league pitchers, and on Monday the A's traded first baseman Matt Olson to the Atlanta Braves. The three trades cut Oakland's projected payroll by about $30 million.
"You see what was happening around here,'' Chapman said of Oakland. "It's sad to leave, but it's happy to go somewhere where it's going to be an incredible opportunity. A lot of emotions, but I think it's going to be an amazing next couple of years.''
Chapman is eligible for arbitration this season and next. He earned $6.54 million in 2021, including a $50,000 bonus for Gold Glove.
The addition of Chapman is the latest move in a busy offseason for the Blue Jays, who lost reigning Cy Young Award winner Robbie Ray and star infielder Marcus Semien as free agents but also signed free-agent pitchers Jose Berrios, Kevin Gausman and Yusei Kikuchi to fortify their starting rotation. Toronto went 91-71 last year but finished one game behind Boston and New York in the AL wild-card race.
"I know how talented they are,'' Chapman said. "It's a team that's ready to compete now, and they're ready to win and go for it. I couldn't be happier to go join that.''
Information from The Associated Press is used in this report.