The right-hander was dealt for relief pitcher Diego Moreno and outfielder Exicardo Cayones.
The trade, first reported Friday, will see the Pirates pay Burnett up to $14 million of the $33 million remaining on his contract, the New York Daily News reported.
New York signed Burnett after the 2008 season, but he struggled to put up wins consistently, compiling a 34-35 mark for the Yanks.
The 35-year-old has posted a career record of 121-111 with a 4.10 ERA in 314 games for the Florida Marlins, Toronto Blue Jays and Yankees.
Moreno, 24, went 2-4 with five saves and a 3.63 ERA in 41 minor-league games last season while the 20-year-old Cayones hit .228 with 12 RBI in 38 Gulf Coast League games.