All three men won Heisman Trophies during their celebrated tenure at the California school.
"We're real excited about J.D.," Carroll said. "A year ago, he was coming back from back surgery. But he's made an effort to get in the best shape of his life. He's faster and stronger than he's ever been."
LSU came in second in the annual coaches' poll, while defending champion Florida was No. 3.
The Big Ten had three representatives in the poll's top 10 as Michigan came in fifth, Wisconsin was ranked No. 7 and Ohio State was No. 10.
Finalizing the top 10 spots were No. 4 Texas, No. 6 West Virginia, No. 8 Oklahoma and No. 9 Virginia Tech.