After years of debate, charges of favoritism, and harangues from fans and members of the media, major college football finally will determine its champion the way virtually every other sport does: on the field.

The 12 university presidents who oversee the sport’s postseason on Tuesday approved a plan to stage a four-team playoff to determine the national championship. The new format, which was announced after a meeting at a Dupont Circle hotel, will go into effect following the 2014 regular season.

Dubbed “a milestone” by some athletic conference commissioners, the playoff will replace the controversial Bowl Championship Series, which used a combination of polls and computer rankings to determine which two teams should play for the national title while also helping to determine the matchups in four other high-profile bowl games.

The former method, which was instituted in 1998, worked fine when two, and only two, teams defined themselves as clearly superior during the regular season. Most years, though, ended with fans of spurned schools lamenting why such a popular sport was determining its champion with computer formulas instead of game results.

Under the new plan, two semifinal games will be played within a rotation of six existing bowls, with the national championship game bid out to a neutral site and managed by the conferences.

“It’s a best-of-both-worlds result,” said Virginia Tech President Charles Steger, the chair of the presidential committee that approved the plan. “It captures the excitement of a playoff but protects the best regular season in sports and also the tradition of the bowls. A four-team playoff doesn’t go too far. It goes just far enough.”

The four playoff participants will be determined by a selection committee, similar to the one that chooses the 68-team field for the highly popular NCAA basketball tournament every March. Details such as the size and composition of the committee remain unresolved, but the criteria it will use will include win-loss record, strength of schedule, head-to-head results and whether a team is a conference champion.

Atlantic Coast Conference Commissioner John Swofford said winning a conference championship would not be a requirement for inclusion in the playoff, but that it would be “at the top of the list of the criteria that the committee is going to be asked to use.” Big Ten Commissioner Jim Delany said the committee likely would consist of “more than 10, less than 20” people.

The semifinal games will be played on New Year’s Eve or New Year’s Day, and the national championship will be held on the first Monday in January that is six or more days after the final semifinal game is played.

In devising the new format, the sport’s leaders aimed to address the fairness complaints while not diluting the significance of what many fans consider the most relevant regular season in big-time college sports. An eight- or 16-team playoff threatened to do that, many felt.

Steger also said the presidents were pleased that this four-team playoff would take place around New Year’s Day and not extend the postseason into a second semester of the academic calendar.

In addition to yielding a competitively satisfying conclusion to the season, the playoff is expected to be highly lucrative. The BCS currently generates about $180 million from its television contract with ESPN, but many observers expect the television rights for the playoff format to be worth more than $400 million when they are put up for bid this fall.

Last week, Bob Boland, the academic chair at New York University’s Tisch School of Sports Management, said the money from television rights fees and neutral site bidding of a national championship game could mirror that of “a second Super Bowl.”

Distribution of that revenue — long an issue of contention during the days of the BCS — remains unresolved. The presidents decided broadly that revenue distribution would reward conferences for success on the field, accommodate teams’ expenses, acknowledge marketplace factors and reward academic performance.

Upstart programs such as Boise State and Utah have long complained that college football’s competitive landscape and revenue distribution have favored traditional powers. Whether the new playoff will address those concerns or whether the rich will continue to get richer remains to be seen, because the selection committee is expected to reward teams for strength of schedule. But Steger said non-BCS conferences were considered during the meeting.

But Tuesday, those issues took a back seat to a move aimed to give fans a “real” champion.

“Historically the Cinderella team is like Cinderella; they don’t show up every day,” Steger said. “But you still want to have that hope and opportunity, and it adds some excitement to it.”