WASHINGTON — The university presidents stood on a stage in a hotel ballroom Tuesday, smiling and satisfied that the college football playoff system the nation had clamored for had been agreed upon in three hours.

After all the controversy surrounding the much-derided Bowl Championship Series, after the annual debates about which teams deserved to play in the national title game, a four-team playoff will be implemented in the 2014 season.

The four semifinalists will be selected by a committee, much as the field for N.C.A.A. basketball tournament is set. No conference will automatically qualify one of its teams. The two semifinal games will be rotated among six bowl sites over a 12-year period, and will be played Dec. 31 or Jan. 1. Those bowls have not been selected.

The championship game will be held at a neutral site, and cities will have the opportunity to bid to host the event. The game will be played on the first Monday in January that is at least six days after the semifinals.