Brackman, 21, was the 30th overall selection, coming to New York from North Carolina State University. He has been assigned to the club's Gulf Coast League affiliate in Tampa, Fla., a Yankees spokesman confirmed.
The Yankees would not disclose financial terms of the contract, but numerous reports have indicated that the hurler is primed to receive a deal in the neighborhood of $4.5 million, including a Yankees-record $3.3 million signing bonus and three one-year team options that could bring the total value of the deal to $13.8 million.
"I feel like the weight of the world is off my shoulders -- for today," Brackman told the North Carolina State University Web site. "Tomorrow, I have to get my things packed up and go to Tampa and see what will happen from there."
A 6-foot-10, 230-pound hurler who also played two seasons of collegiate basketball as a center and forward, Brackman was 6-4 with a 3.81 ERA in 13 starts as a junior at North Carolina State, striking out 74 and walking 37 in a career-high 78 innings.
Brackman drew concerns before the Draft due to an injured pitching elbow that cut short his season. He has traveled to Birmingham, Ala., where he planned to finalize the contract before undergoing Tommy John elbow reconstruction surgery under the care of noted orthopedic surgeon Dr. James Andrews. The procedure would likely put Brackman out of action for the 2008 season.
Brackman's signing capped an eventful day for the Yankees, who entered Wednesday with a Major League-high six of their top 10 selections still unsigned.
New York first made progress with all of its other high-level picks below Brackman, with general manager Brian Cashman announcing the signings of several players immediately following the club's 6-3 loss to the Baltimore Orioles.
At Yankee Stadium, Cashman said that the contracts of second-round catcher Austin Romine, fourth-round third baseman Bradley Suttle, sixth-round catcher Richard Weems and 10th-round shortstop Carmen Angelini were all finalized on Wednesday.
Brackman was the only draftee the Yankees were still negotiating with as Wednesday's 11:59 p.m. ET deadline neared. With his deal, New York signed 34 of its 50 players it selected in the June First-Year Player Draft.
"In the last 48 hours, we entered a situation where we were really trying to flush it out and see how realistic it was going to be or not," Cashman said.
In order to make room for Brackman on the Yankees' 40-man roster, the club designated Chris Basak for assignment. The 28-year-old infielder appeared in five games this season for New York, flying out in his only at-bat on June 24.
Basak had been playing for Triple-A Scranton/Wilkes-Barre of the International League, where he was batting .253 with seven home runs and 38 RBIs in 84 games.
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.