Elway, a redshirt freshman quarterback, will remain at Arizona State as a student, however.
"He's just tired of football and wants to do something else with his life," Sun Devils coach Dennis Erickson said Monday, according to The Arizona Republic. "He made a decision, and we all understand it. He would have played here eventually."
Elway, who was in a five-way battle for the starting quarterback job this fall, was considered to be behind senior Danny Sullivan and redshirt sophomore Samson Szakacsy on the depth chart, with sophomore Chasen Stangel and freshman Brock Osweiler also in the mix.
Elway, out of Cherry Creek (Colo.) High School, did not play in a scrimmage last weekend.
"He would have played here eventually," Erickson said.