Robert McClendon, 52, was released by Franklin County Common Pleas Judge Charles Schneider, who cited the DNA test.
"You know, you go through times where you feel it might not happen, but you never, ever give up hope," McClendon said after his release. "You don't ever use the word, 'never happen.' It's not healthy."
McClendon's relatives and supporters cheered and embraced McClendon upon his release, when he met his 20-year-old daughter Rahshea' Knaff and 9-month old granddaughter Sa'Rai Shelton for the first time.
Jennifer Bergeron, a lawyer with the Ohio Innocence Project, said she expects prosecutors to formally drop charges against McClendon within the next two weeks.
"To be in prison for 18 years for something you didn't do and then know you are going to walk out of court a free man, that's a lot to take in in one day," Bergeron said.
Franklin County Prosecutor Ron O'Brien said he didn't think the case would go to a new trial.
McClendon planned to go to the home of a relative in Columbus on Monday to celebrate his release at a dinner with about 50 supporters, friends and relatives, said Mark Godsey, faculty director of the Innocence Project.
McClendon said he eventually wants to get a good job, maybe start a business and, if he's needed, speak publicly about DNA testing.
"This is not just about me," he said. "I believe that there are others in prison like me, and then there are others in prison who are guilty. You've got to give it a chance to work."
McClendon, who denied raping the girl, was convicted in 1991 and sentenced to 15 years to life in prison. He was denied parole in 2007.
DNA Diagnostics Center, a lab north of Cincinnati, agreed to conduct tests on McClendon and other inmates for free as a public service after The Columbus Dispatch published a series in January featuring 30 inmates whose applications for new DNA testing had been stalled.
The newspaper's investigation also found flaws in the state's DNA testing system: Police and courts routinely discard evidence after trials, and prosecutors and judges often dismiss inmate applications for DNA testing without a stated reason.
In McClendon's case, authorities had long since lost or thrown away swabs from the victim's medical exam - typically the best evidence for testing rape cases - but agreed to provide the lab with the girl's underwear.
Using new technology unavailable at the time of the crime, the lab found faint traces of semen that didn't match McClendon's DNA profile, the Innocence Project announced last month.
Prosecutors said McClendon took a 10-year-old relative from her backyard, blindfolded her, drove her to a house and raped her. The victim reported the rape the next day and was taken to a hospital.
McClendon was convicted largely on the victim's testimony, Bergeron said. There was no physical evidence to tie him to the crime, she said. He was previously convicted in the 1970s of attempted corruption of a minor for having sex with a 15-year-old girl when he was 19.