Kenneth W. Starr, the former independent counsel who delivered a report that served as the basis for President Bill Clinton’s impeachment in 1998, was removed as president of Baylor University on Thursday after an investigation found the university mishandled accusations of sexual assault against football players.

The university also fired the football coach, Art Briles, whose ascendant program brought in millions of dollars in revenue but was dogged by accusations of sexual assault committed by its players — an increasingly familiar combination in big-time college sports.

Mr. Starr was stripped of his title as university president but will remain Baylor’s chancellor and a professor at the law school. The chancellor position is “centered around development and religious liberty,” a regent said on a conference call Thursday afternoon, adding that Mr. Starr’s “operational responsibilities have been removed.”

Mr. Starr’s demotion delivered a twist to the biography of a man whose reputation was built on what many considered an overzealous pursuit of allegations of sexual transgressions by Mr. Clinton. Now he is being punished for leading an administration that, according to a report by an outside law firm commissioned by the university’s governing board, looked the other way when Baylor football players were accused of sex crimes, and sometimes convicted of them.