Smith, a redshirt sophomore, set a Missouri season record with 11.5 sacks his freshman season and was Big 12 Conference defensive freshman and newcomer of the year. Last season, he missed three games due to a broken leg and had 5.5 sacks along with 48 tackles, 10 of them for loss.
"I'd like to thank everyone at Mizzou for supporting me," Smith said in a statement. "The coaches, our fans and alumni, everyone has been great, and they've definitely helped me get to this point. It's been my dream for as long as I can remember to play in the NFL, so this is something I'm really excited for."
Like quarterback Blaine Gabbert, who made himself available for the NFL draft on Monday, Smith will forgo his final two seasons of college eligibility.
Coach Gary Pinkel called Smith "one of the most gifted athletes in the country at his position."
"We'd love to have the chance to coach him longer, but we're 100 percent behind him and supportive with this decision," Pinkel said.
Missouri has had 15 players drafted during the past six years, including six in 2010.
Clay had 1,012 yards rushing and 14 touchdowns this season, but saw his workload decrease because of injury and the emergence of fellow running backs James White and Montee Ball.
"This is the right decision for me at this time and I'm excited to start a new chapter," Clay said in a statement Friday.
Clay finished his Badgers career seventh in school history with 3,413 career yards rushing and fifth with 41 career touchdowns.
"There are a lot of people that I would like to thank who have helped me along the way," Clay said. "I'd like to thank the great Wisconsin fans for supporting me throughout my time as a Badger. I'd also like to thank my family for helping me through this process."
Coach Bret Bielema wished Clay the best.
"Since coming to Wisconsin, John has gone above and beyond all of our expectations both on and off the field," Bielema said. "His tremendous production on the field speaks for itself, but we are also proud of him as a teammate and the work he has done in the classroom and off the field. We support his decision and wish him luck."
Badgers defensive end J.J. Watt also applied for the draft this week. The Badgers ended the season 11-2 after a 21-19 loss to Texas Christian in the Rose Bowl.
Copyright 2011 by The Associated Press