Oz is not the only high-profile name on the council, which also includes New England Patriots coach Bill Bellichick, as well as bodybuilder and actor Lou Ferrigno, known for playing the Incredible Hulk.
Along with Belichick, Axios reports the president will appoint several other celebrities to the council, including the beach volleyball legend Misty May-Treanor, the Yankees closer Mariano Rivera, and the Heisman Trophy victor Herschel Walker.
Snyder, who was nominated for a two-year term on the council, was part of a large group of nominees presented by President Trump on Friday.
Trump appeared on Dr. Oz's show during the 2016 campaign to discuss his health and reveal the results of a brief health evaluation by his then-doctor Harold Bornstein.
The naming of the council's members comes several months after Trump signed an executive order shuffling the name of the body so the word "sports" came first. It was the team's fifth Super Bowl victory since 1960.
The Sport, Fitness, and Nutrition council will advise President Trump on opportunities for expanding participation in sports.
"It's sad what's happened with all the kneeling and standing and all that, because Donald Trump is a great man, he's a great president and I wish people could understand that", Walker said in an interview with Fox News before the game.
President Donald Trump is bringing in big league players to his fitness council.