"We got him," said state police Sgt. Craig Stine, commander of the Schuylkill Haven barracks.
Geiger was arrested by state police as he left his home to go to work. He was scheduled to be arraigned at 12:30 p.m. Thursday on charges of third-degree murder, voluntary manslaughter, abuse of corpse and tampering with evidence.
The circumstances of Reed's killing weren't immediately clear, and police didn't immediately say what led them to Geiger.
Police and prosecutors planned a news conference later Thursday to discuss the arrest.
Until recently, Reed's death had been classified as "undetermined," but officials ruled in early July that it was a homicide after studying his remains.
State police exhumed the body in January after turning up new evidence that led them to conclude the brown-haired, blue-eyed teen was a victim of foul play. Reed's family had welcomed the renewed attention, saying the original investigation was inadequate, and said Thursday that they were pleased an arrest had finally been made.
"I think it's long overdue and I'm glad they finally found whoever did this ... so that my nephew can finally be resting in peace," said his aunt, Judy Adams, who lives nearby.
Reed's badly decomposed remains were found in a remote thicket on the edge of town in December 1985, about a half-mile from his bicycle.
Although police labeled the death suspicious, their investigation stalled after an inconclusive autopsy.
The boy's remains were examined this year by Dr. Anthony Falsetti, a forensic anthropologist at the University of Florida, who spent about a month analyzing them. Two anthropologists who had initially theorized the boy might have succumbed to an undiagnosed case of diabetes now concur with Falsetti's findings, the coroner said.
Reed's father died when he was a toddler, and his mother died in 2001. A sister who encouraged police to pursue the case, Virginia Meadows, died last year.
"The feeling is hard to describe. After all these years, I never thought it would come down to this. You give up hope," said David's brother, Joseph Reed, of Fort Myers, Fla.
Reed said he was barely acquainted with Geiger but that he had been considered "pretty normal" around Schuylkill Haven, a small town about 75 miles northwest of Philadelphia.
In the months after Reed's disappearance, Reed said, Geiger "would say 'Hi,' like nothing happened. I wish I knew back then what I know today."