The Reds received minor league catcher Chase Weems in the deal.
Hairston confirmed he was traded before the Reds' scheduled game against the Colorado Rockies. He is batting .254 with eight homers and 27 RBIs, having played shortstop, second base, third base and all three outfield positions this season.
"He is a guy that can play pretty much anywhere," Yankees manager Joe Girardi said in Chicago. "Probably the only place I wouldn't put him is behind the dish. He gives us a lot of flexibility, a right-handed hitter for days that we can give a lefty off."
With speedy outfielder Brett Gardner on the disabled list with a broken thumb, the Yankees moved to shore up their bench. Hairston gives the AL East leaders an experienced player who could spell several stars, including third baseman Alex Rodriguez, shortstop Derek Jeter and left fielder Johnny Damon.
"Whatever they ask me to do, I'll do it," Hairston said. "I can play anywhere."
It was the Reds' first trade of the week and caught Hairston by surprise. Other teams had been interested in Cincinnati's relievers.
"I'm a little shocked right now," he said. "I feel a closeness with these guys. At the same time, I'm going to New York where we have a chance to win."
However, with the Yankees having won 11 of 14 since the All-Star break and holding a 2 1/2-game lead over their AL East rivals, first baseman Mark Teixeira wasn't worried.
"They made their team better and it's going to continue to be a great battle," he said. "We have everything we need to win here and I think we're showing that."
Duncan was batting .268 with 25 home runs and 75 RBIs in 90 games at Triple-A. He is a career .221 hitter with 8 homers 23 RBIs in 57 games split between 2006 and 2007.
Albaladejo was 4-1 with a 5.61 ERA in 22 appearances for the Yankees.
The 20-year-old Weems was batting .260 with a homer and 14 RBIs in 55 games with Class-A Charleston this season. He was picked in the sixth round of the 2007 draft.