Roberson was identified as a suspect in a sexual assault said to have taken place in a motel in suburban Phoenix, one day before the Wildcats were to play Ohio State in the Fiesta Bowl. He claimed there was sex with a 22-year-old woman, identified as a KSU alumnus, but that it was consensual.
The case was being investigated by the sheriff's department in Maricopa County (Ariz.), whose county attorney says charges will not be pursued.
Coach Bill Snyder offered an apology in an open letter.
"I am extending a heartfelt and sincere apology to the people of Kansas State and entire state," Snyder said. "I cannot adequately convey to you how badly I feel for those within the Wildcat family."
Roberson, a senior who has no eligibility left, will not receive a Fiesta Bowl ring. He did not play well against the Buckeyes, who won, 35-28.