WASHINGTON — College football will finally have a playoff. Come 2014, the BCS is dead.

A committee of university presidents on Tuesday approved a plan for a four-team playoff put forward by commissioners of the major football conferences.

The move completes a six-month process for the commissioners, who have been working on a new way to determine a major college football champion after years of griping from fans.

“There were differences of views,” said the Virginia Tech president, Charles W. Steger. “It would be a serious mistake to assume it was a rubber stamp.”

Instead of simply matching the nation’s No. 1 and No. 2 teams in a championship game after the regular season, the way the Bowl Championship Series has done since 1998, the new format will create a pair of national semifinals.

College football fans have been clamoring for a playoff for years, and the BCS has been a constant target for criticism. Lawmakers have railed against it. A political action committee was formed, dedicated to its destruction. The Justice Department looked into whether it broke antitrust laws. Even President Obama said he wanted a playoff.

Now it’s a reality.

No. 1 will play No. 4, and No. 2 will play No. 3 on Dec. 31 and Jan. 1. The sites of those games will rotate among the four current BCS bowls – Rose, Orange, Fiesta and Sugar – and two more to be determined.

The winners will advance to the championship game on the first Monday in January that is six or more days after the last semifinal. The first championship Monday is Jan. 12, 2015.

The site of the title game will move around the way the Super Bowl does, with cities bidding for the right to host.

The teams will be selected by a committee, similar to the way the NCAA basketball tournament field is set. The men’s tournament has 68 teams.

The football committee will have a much tougher task, trying to whittle the field down to four. The factors to be considered will include won-loss record, strength of schedule, head-to-head results and whether a team is a conference champion.

The commissioners want to lock in this format for 12 years with a television partner. The current BCS deal with ESPN runs through the 2013 season.