Burnett, a 31-year-old former eighth-round pick in the 1995 MLB draft by the New York Mets, compiled an 18-10 record with a 4.07 ERA and a career-high 231 strikeouts in 221 2/3 innings last season.
He left the Blue Jays after completing three years of a five-year deal worth $55 million.
Despite numerous shoulder and elbow injuries in a 10-year career with Toronto and the Florida Marlins, Burnett has an 87-76 record, with a 3.81 ERA and 1,278 strikeouts in 1,376 1/3 innings (211 starts).
It was the Yankees' second signing of a high-priced pitcher this week.
On Wednesday, left-hander CC Sabathia agreed to a deal worth $161 million over seven years.
"We obviously have a need to improve our starting rotation, period," Yankees General Manager Brian Cashman told the New York Daily News this week.
Exploding whale video goes viral on Internet
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club