Yankees general manager Brian Cashman announced the move on Tuesday during a conference call with reporters.
Brackman, 25, got his first taste of Major League duty this September with three scoreless appearances spanning 2 1/3 innings, while permitting three walks and a hit.
The 6-foot-11 hurler was 3-6 with a 6.00 ERA in 33 appearances (13 starts) with Triple-A Scranton/Wilkes-Barre, issuing 75 walks and striking out 75 in 96 innings. He allowed 65 runs (64 earned) and 82 hits.
Brackman signed a four-year, $4.55 million deal after being taken 30th overall in the 2007 First-Year Player Draft from North Carolina State University and missed all of '08 after undergoing Tommy John surgery on his pitching elbow.
Brackman compiled a record of 15-29 with a 5.11 ERA in 89 Minor League games (58 starts) from 2009-11, pitching at four different levels in New York's system.