By Larry Fine
Left-handed reliever Boone Logan also arrived from Atlanta in exchange for Cabrera, left-handed pitcher Michael Dunn, right-hander Arodys Vizcaino and cash, said the World Series champion Yankees.
Vazquez, who finished fourth in 2009 National League Cy Young Award voting, joins CC Sabathia, AJ Burnett, Andy Pettitte and Joba Chamberlain or Phil Hughes in New York's starting rotation.
The 33-year-old Vazquez, who went 15-10 with a 2.87 earned run average last season, also pitched for the Yankees in 2004 when he went 14-10 with a 4.91 ERA before being traded to Arizona in a deal for left-hander Randy Johnson.
Logan, 25, was 1-1 with a 5.19 ERA in 20 relief appearances with Atlanta.
The Braves traded one of their starting pitchers to shore up other areas of the team after they signed starter Tim Hudson to a long-term contract in November.
Cabrera, 25, set career highs with 28 doubles and 13 homers in 2009 as he batted .274. The switch-hitter had three walk-off hits, delivering the winning runs in the final at-bat of three New York victories.
"Melky will fit in our club very well," Braves general manager Frank Wren told reporters.
"He can play all three outfield positions, has postseason experience and is a switch-hitter with a really strong throwing arm who can defend. That versatility really helps our ballclub."
Dunn, 24, went a combined 4-3 with two saves and a 3.31 ERA in 38 relief appearances last season in Double-A and Triple-A minor leagues and was named an Eastern League All-Star.
Vizcaino, 19, was 2-4 with a 2.13 ERA in Single-A.
"Arodys is a special young pitcher. We had to have him in the deal," Wren said.
(Editing by Tony Jimenez)