Brackman was the New York Yankees' first-round pick in 2007 even though they knew he needed reconstructive elbow surgery. He had the operation nine days after signing. He went 15-29 in 58 starts and 31 relief appearances in the minors from 2009-11 with a 5.11 ERA.
The Yankees called up the 6-foot-10 Brackman last September and he pitched in three games. They declined his contract option after the season.
Brackman would be paid $500,000 by the Reds if he's in the major leagues and $480,000 if he's in the minors.
The Reds also announced that their pitchers and catchers will report and have their first spring training workout in Goodyear, Ariz., on Feb. 19. The rest of the squad will report and work out on Feb. 24.