"It's my time to go," Watson, who was named offensive MVP of the title game, told reporters.
The junior went 36-for-56 for 420 yards and three touchdowns, and ran for 43 yards and a fourth touchdown in Clemson's 35-31 win. He found Hunter Renfrow for a 2-yard touchdown pass with one second remaining to give the Tigers their first national championship since 1981.
Watson was a Heisman Trophy finalist the past two seasons, finishing third in 2015 and second in 2016. ESPN's Mel Kiper Jr. has Watson ranked third among quarterbacks for the upcoming draft.
"Whoever picks me up is gonna get a champion, not just on the field, but off the field, and just a champion at heart who'll make people around him better," Watson told ESPN's Scott Van Pelt after Monday night's win. "I'm just gonna go to work, and regardless of my situation or where I go, I'm gonna play my role and do the best I can do."
Clemson is still waiting on an answer from wide receiver Artavis Scott, who said after the game that he is not ready to declare his intentions.
"I'm not sold yet if I want to leave or if I want to stay," Scott said. "I ain't in no rush and I ain't going to say I ain't going to leave, but I've got a lot of stuff to talk about with my family and see what I'm going to do."
Receiver Mike Williams and running back Wayne Gallman previously announced they are leaving Clemson early.
ESPN's Andrea Adelson and The Associated Press contributed to this report.