Chris Lane, 23, a student at East Central University in Ada, was shot while jogging, the Duncan Banner reported Sunday.
Duncan police arrested the juveniles, age 15, 16 and 17, about four hours after the Friday afternoon shooting.
Police Chief Danny Ford said a Duncan resident called about 7:05 p.m. and said there were juveniles at a residence who "were wanting to kill somebody."
A dismantled shotgun was found at the scene of the arrest, but police determined it was not the weapon used in Lane's shooting.
Ford said postings on the teens' Facebook page appeared to indicate they had recently killed a dog.
He said the suspects decided to kill Lane when they saw him run by. "It was random," Ford said.
Lane, a member of the university's baseball team, had returned from Australia only three days before. He was staying with his girlfriend and her family.
The juveniles, whose names were not released, are being held on first degree murder charges, the police chief said.