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.