Burnett's agreement was confirmed by the office of his agent, Darek Braunecker, The Associated Press reported.
While Yankees general manager Brian Cashman and Braunecker are still negotiating final contract terms, the deal is expected to be complete once Burnett passes a physical.
Burnett, who turns 32 in January, will join CC Sabathia at the top of a revamped starting rotation in New York. The Yankees agreed to terms on a seven-year, $161 million contract with Sabathia earlier this week.
"I can sense the excitement and the confidence that's spreading around the entire organization about what we're getting done and what we may get done still," Yankees co-chairman Hank Steinbrenner told The Associated Press Friday before Burnett's decision became known. "A rising tide lifts all boats, and the confidence and the excitement right now among the team and the organization is contagious."
The Yankees made a late charge to beat out the Atlanta Braves for Burnett, who went 18-10 with a 4.07 ERA in 35 starts with Toronto this season. Burnett won 10 of his last 12 decisions. He set career highs in wins, strikeouts (231) and innings (221 1/3).
New York is still looking for one more starter, and Cashman left the winter meetings in Las Vegas this week to meet with longtime Yankee Andy Pettitte.
In December 2005, Braunecker and his agency, Frontline Athlete Management, negotiated a five-year, $55 million deal for Burnett that included an opt-out clause after three seasons. It was the first opt-out provision ever in a pitcher's contract.
Between the money that Burnett earned in Toronto and the guaranteed $82.5 million that he's scheduled to receive from the Yankees, his contracts will amount to $113.5 million over eight seasons.
The addition of Sabathia and Burnett as free agents -- combined with Chien-Ming Wang's expected return to full health from a foot injury -- gives New York a top of the rotation that can stack up with Josh Beckett, Jon Lester and Daisuke Matsuzaka in Boston.
Burnett and Sabathia combined to go 35-20 with a 3.34 ERA this season. Yankees starters, in contrast, posted a 59-53 record with a 4.58 ERA. That includes the first 20-win season by Mike Mussina, who recently retired.
Although Burnett's numbers haven't always matched his talent, some scouts and front-office people think he made significant strides this season as the No. 2 starter in Toronto behind Roy Halladay.
Burnett also has a strong track record within the American League East. He's 20-5 with a 3.29 ERA against New York's divisional opponents in Tampa Bay, Boston, Baltimore and Toronto.
Jerry Crasnick covers baseball for ESPN Insider. The Associated Press contributed to this report.