CHICAGO — Jameis Winston, the star quarterback from Florida State who played under a swirl of controversy, was chosen first over all in the N.F.L. draft by the Tampa Bay Buccaneers on Thursday.

Winston led the Seminoles to a national championship during the 2013 season and was considered, along with Oregon quarterback Marcus Mariota, to have the best chance of being chosen first.

Success has come quickly for Winston, the youngest player to win the Heisman Trophy, who was also drafted by the Texas Rangers. But he has been dogged by accusations that he raped a former Florida State student, who has since filed a civil suit against him.

Winston’s off-field problems proved to be a source of consternation for the N.F.L., which has tried to clean up its image as a league willing to tolerate violence and lawbreaking off the field. Several weeks ago, Winston met Commissioner Roger Goodell to discuss his future in the league.