Cotton Bowl Athletic Association chairman Bruce Gadd declined to reveal details of the contract with the Cowboys but said it will last more than a decade.
"This is one of the most important decisions in the 71-year history of the AT&T Cotton Bowl," Gadd said in a statement. "Moving the Classic preserves the Classic's legacy and, at the same time, secures its future as one of college football's best postseason bowl games."
Backers want to get the Cotton Bowl into the Bowl Championship Series mix and make it the future location of a national title game.
The move was approved by a voice vote during a somber regular meeting of the Cotton Bowl Athletic Association board of directors, Gadd said. He said no negative votes were voiced, although some board members may have declined to vote.
"There were tears in the room," he said. "When it was over it was unanimous, and there was some applause. ... It was a move we had to make. There was not one incident of someone standing up and saying maybe we shouldn't do this."
The first game at the new venue in Arlington, located between Dallas and Fort Worth, will be New Year's Day, 2010.
"It's unfortunate. It's disappointing, but it's not surprising," Dallas Mayor Laura Miller said. "It has always been a hard sell for us to keep the Classic because we don't have the one thing they want _ a roof. I begged them not to do it, but that's their call."
Plans for the $1 billion stadium, scheduled to open in 2009, include a retractable roof that would cover a hole similar to the one at Texas Stadium in Irving.
A domed stadium is important to bowl game officials because of Dallas' sometimes cold January weather. Gadd said weather was a key factor that kept the Cotton Bowl from being included in the BCS when the postseason format was adopted in 1994.
"As anyone can imagine, this decision was difficult, but after completing our due diligence, we determined that a move to the new stadium would remove all weather concerns, keep us competitive in a changing college postseason landscape and provide a world-class facility for our partners, the players and fans," Gadd said.
The game, first played in 1937, has always been held at the Cotton Bowl, which opened in 1932. The stadium is also home to the annual Texas-Oklahoma and Grambling State-Prairie View A&M games. Both are under contract there through 2010.
Gadd said the game's name won't change because it is trademarked by the association.