Christopher Newton, 37, who declined to seek any appeals in his case and did not ask Gov. Ted Strickland for clemency, had no late legal actions pending, said Leo Jennings, a spokesman for Attorney General Marc Dann.
Newton was at the Southern Ohio Correctional Facility in Lucasville, where he is scheduled to die by lethal injection.
Newton refused his breakfast Thursday morning and was calm, after sleeping about five hours overnight, state prisons spokeswoman Andrea Dean said. He then met with his sister, his spiritual adviser and his attorney.
Newton, who had been incarcerated for a parole violation on an attempted burglary conviction, beat cellmate Jason Brewer to death in 2001. He said he killed Brewer, 27, because he repeatedly gave up while they were playing chess.
"He kept giving up. Every time I put him in check, he'd give up and want to start a new game," Newton told reporters in April. "And I tried to tell him you never give up ... I just got tired of it."
Newton had intentionally left a hand print during an attempted burglary of his father's home while on probation so he would get caught, hoping to return to the structure of prison. Once back in prison, he killed Brewer by slamming his head onto the floor, stomping his throat and cutting a piece from his orange prison suit to strangle him.
Court documents indicated Newton knew killing Brewer was a capital crime, and he later refused to cooperate with investigators unless they sought the death penalty against him.
"He's certainly the epitome of a volunteer," Jennings said.
Newton would be the second inmate executed since Strickland took office in January and the 26th since the state resumed executions in 1999.
The choice of the city of Helsinki is not incidental as the capital of Finland had hosted US-Soviet negotiations on the limitation of nuclear stockpiles in 1969