It's the first time college football's top award was returned by a recipient.
"While this decision is heart-breaking, I find solace in knowing that the award was made possible by the support and love of so many," Bush said. "Those are gifts that can never be taken away."
USC was hit with heavy sanctions by the NCAA this summer after it determined Bush had received improper benefits. The NCAA ruled that Bush was ineligible for the 2005 season, which opened the possibility that the Heisman Trophy Trust would take back the award.
One of the few guidelines given to Heisman Trophy voters is that a player must be in compliance with NCAA rules to be eligible for the trophy.
There was no immediate word from the Heisman Trust if the award would be vacated or given to Young.