"To me, there would be no greater goal than to help win a World Series for the New York Yankees," Henson said at a news conference in Brighton, Mich. "I will keep memories of the University of Michigan close to my heart."
Henson is to report to the Yankees on Monday and is expected to resume his baseball career at triple-A Columbus.
"He, obviously, has terrific potential, and he's a future superstar, there's no question," Yankees manager Joe Torre said.
Henson originally was drafted by the Yankees in 1998 and played in their minor-league system, then was dealt to Cincinnati last July as part of the trade that brought Denny Neagle to New York.
Convinced they couldn't sign him, the Reds traded Henson back to New York on Wednesday, along with outfielder Michael Coleman for outfield prospect Wily Mo Pena.
"We were at such a time last year where we needed a starting pitcher," Torre said. "When you're with the Yankees, the future is always now, but we were fortunate enough to have the future be now and then tomorrow again in getting him back."
Henson, who likely would have been a first-round NFL draft pick in 2002, led Michigan to a 9-3 record and No. 11 ranking last season. Before the trade, he was planning to return to the Wolverines for his senior season.
"We wish him well," Michigan coach Lloyd Carr said in a statement.
Henson hit .266 with nine homers in 308 at-bats last season, mostly in double A. He struggled after the trade, hitting .172 in 16 games for the Reds' double A Chattanooga team.
New York now has two potential replacements at third base for Scott Brosius, whose contract expires after this season. At the start of spring training, the Yankees signed Cuban defector Andy Morales, who probably will be moved to the outfield.
The Yankees pushed for Henson to give up football immediately. They would not have offered a long-term commitment unless he gave up his senior season at Michigan.
"We worked hard at it and got it done late last night," Yankees general manager Brian Cashman said Saturday.
At an average annual value of $2.83 million, the Yankees would wind up with a bargain if Henson turns into a baseball star. If he starts 2002 with the major-league team, he would be eligible for salary arbitration for only one year, 2007, before becoming eligible for free agency.
In addition, the deal is backloaded, with Henson getting about $10 million in the final two seasons.