Karageorge, 22, was found dead in a dumpster of an apparent self-inflicted gunshot wound. He was identified by tattoos at the scene, and a police spokesman said the investigation would continue with both the dumpster and the body of Karageorge being transported to the county morgue.
"At this time, there's a lot of questions that we're still trying to work out," Sgt. Rich Weiner told reporters at the scene. "But he was found inside of the dumpster, the handgun was found inside of the dumpster with him.
"At this time we are able to confirm through tattoos here at the scene that it is the body of Kosta Karageorge."
Coach Urban Meyer wouldn't address the situation in his weekly news conference on Monday, but Ohio State issued a statement, saying: "We know that many of you are concerned, as we are, about the tragic news that we received yesterday about the death of one of our student-athletes, Kosta Karageorge.
"It is very early in the process of determining the cause of death, and the Columbus division of police is still investigating. We are unable to discuss this situation in detail at this time. The investigation continues, we are also not able to comment on student-athlete's medical treatments.
A police report says Karageorge's mother told authorities he has had concussions and spells of confusion. She said he texted a message Wednesday citing the concussions and saying he was sorry if he was "an embarrassment."
Karageorge was scheduled to be recognized on senior day during Saturday's home game against rival Michigan, but he had gone missing on Wednesday leading up to the 42-28 win by the No. 6 Buckeyes.
Karageorge had previously spent three seasons on the Ohio State wrestling team before walking on to help on the defensive line in August.
Wrestling coach Tom Ryan tells The Columbus Dispatch that Karageorge had no documented concussions as a wrestler.
Ryan said teammates wondered if they could have intervened to help Karageorge, and some wept at the news of his death.
"There was a lot of crying," Ryan told the newspaper. "That says something because you know how men are. We don't cry in front of anybody and don't show weakness. But it was emotional."
Ryan said many on the team wondered if they could have done anything to prevent the tragedy.
"I've been doing this for 22 years. This is as tough as it gets," he said.
Some teammates attended a vigil on campus Sunday night that drew a crowd of up to several hundred people.
Information from The Associated Press was used in this report.