The conferences made the announcement Tuesday. The agreement between the leagues and the bowl is for 12 years, and ESPN will hold the TV rights.
The SEC has a long history with the Sugar Bowl. Seventy-one times an SEC team has played in the game, far more than any other league. The very first Sugar Bowl in 1935 matched Tulane, then of the SEC, against Temple.
"New Orleans and the Sugar Bowl are synonymous with post-season college football. For many years, fans have enjoyed the color and pageantry that New Orleans offers," SEC Commissioner Mike Slive said in a statement. "We look forward to competing against the Big 12 as a new championship tradition begins on New Year's Day."
The agreement was first reported by ESPN.com, which also reported that ESPN will pay $80 million per year to televise the game.
Several sites were vying to host the game, including Cowboys Stadium in Arlington, Texas. Atlanta, Houston and San Antonio also submitted bids, but it came down to the Cotton Bowl in Arlington and the Sugar Bowl in New Orleans.
"It was a very difficult decision," Big 12 Commissioner Bob Bowlsby told the AP in a phone interview Tuesday night.
He declined to parse the decision, but did say many factors were considered, from facilities to hotel space. He said despite the SEC's long relationship with the Sugar Bowl, Texas got strong consideration.
"If think if it would have gone to Dallas, the SEC would have been fine with it," he said.
The new college football playoff begins after the 2014 season and the first Sugar Bowl in the new format will be played Jan. 1, 2015. It will match the champions from the SEC and Big 12, unless those teams are selected to the national semifinals. In that case, two other highly rated teams from those conferences will be paired up.
"We're pleased to have been selected to host this great game," Sugar Bowl Chief Executive Officer Paul Hoolahan said. "This gives us the chance to extend the Sugar Bowl's long-standing relationship with the Southeastern Conference and to develop a new relationship with the Big 12 Conference."
The game will be part of the semifinal rotation for the new playoff system, along with the Rose Bowl and the Orange Bowl. The Big Ten and Pac-12 will continue their longtime relationship with the Rose Bowl, and the Atlantic Coast Conference has a deal to send its champion or another highly ranked team to the Orange Bowl.
Another deal is being worked on that will send a team from either an SEC team, a Big Ten team, or Notre Dame to the Orange Bowl to face the ACC in years the Miami-based bowl does not host a national semifinal.
At least three more sites need to be picked, and the Cotton Bowl is likely to be one of them.
"Regardless of which site we chose, the other city is likely to host an access bowl, to host semifinals and will be considered to host the championship game," Bowlsby said.
The Fiesta Bowl in Glendale, Ariz., is expected to be in the playoff rotation, and Atlanta, which hosts the Chick-fil-A Bowl, is the other leading candidate to be part of the new postseason system. How often each site hosts a semifinal has yet to be determined.
There is also a plan being considered to add a seventh game to the rotation that would match either a Pac-12 or Big 12 team against the best team from the five other FBS conferences, including the Big East.
"Both a seven-game and a six-game model are still in play," Bowlsby said.