Hawkins' deal is subject to him passing a physical, a baseball official familiar with the negotiations said Sunday, speaking on condition of anonymity because the contract has not been finalized.
The right-hander, who will be 35 on Dec. 21, was 2-5 with a 3.42 ERA last season for the Colorado Rockies. He made $3.25 million and Colorado declined a $3.75 million option, choosing to pay a $250,000 buyout.
New York's middle relievers struggled last season, with Kyle Farnsworth and Luis Vizcaino pitching inconsistently for long stretches and the Yankees converting Joba Chamberlain, a starter in the minors, into a reliever for the final two months of the season. Chamberlain became Mariano Rivera's primary setup man, but New York plans on including Chamberlain in its starting rotation next year.
Yankees general manager Brian Cashman said he hoped to re-sign Vizcaino, who on Friday declined the team's offer of salary arbitration.
Hawkins pitched for the Minnesota Twins from 1995-2003, then moved on to the Chicago Cubs, San Francisco Giants, Baltimore Orioles and the Rockies. He made five postseason appearances this year, allowing one run and one hit in five innings.
His decision to sign with the Yankees was first reported by foxsports.com.