Philip Scott Fournier, 55, was arrested Friday, in the beating death of Joyce McLain, according to Col. Robert Williams of the Maine State Police.
McLain, a well-liked student training for soccer season, left her home and went for a jog on in August, 1980, Williams said. She was 16 at the time.
Her body was found near a power line behind a high school two days later.
The case remained cold for more than three decades.
In 2008, McLain's body was exhumed and detectives from the state police crime laboratory and the major crimes unit reviewed old and new evidence, Williams said.
It wasn't until Friday that authorities were confident they had enough evidence to bring a charge to trial and prove it beyond a reasonable doubt, he added.
"Right now we're confident we have the person that committed the homicide," Williams said in a news conference.
"Over the years, Fournier has made statements to a number of people indicating potential knowledge and involvement in the death of Joyce McLain," Williams added.
Fournier was 19 at the time of McLain's murder.
Williams said that Fournier's name has been mentioned in police reports since the beginning of the investigation and that the suspect "knew of" McLain before she was killed.
Fournier was arrested Friday without incident and is being held without bail on a murder charge. He appeared in court Monday, where he did not enter a plea.