Citing a person briefed on Newton's situation, the newspaper said the presumed Heisman Trophy front-runner left the school rather than face a suspension or expulsion, partly due to three alleged instances of cheating.
The Times report comes after allegations by former Mississippi State quarterback John Bond that a man connected to an NFL agent had been shopping Newton's services to colleges for a "specified payment," reportedly $180,000.
"I'm not going to respond to every story or criticism that is reported by the media," Newton told the Times. "I've talked on several occasions about my time at Florida."
Newton, who denies any wrongdoing, has said his departure from Florida was due to the return of the Gators' star quarterback, Tim Tebow, for his senior season in 2009.
But Foxsports.com reported that Newton wasn't even enrolled at Florida at the time of Tebow's return and was actually facing suspension or expulsion.