Moira Anderson, 11, disappeared in 1957 after she took a bus to buy a card for her mother. Alexander Gartshore admitted she was a passenger on his bus but said she was alive when he last saw her, the Scotsman reported.
Lord Advocate Frank Mulholland released evidence gathered by a police cold case unit that would have been used if Gartshore was still available for trial.
"This will hopefully bring closure to the family of Moira Anderson who have had to wait more than half a century for answers," he said. "I would like to pay tribute to the campaigners who refused to allow the memory of Moira Anderson to become forgotten."
Last year, police searched the grave of one of Gartshore's friends, a man who died in 1957, for Moira's body. They found nothing, but new witnesses who saw news stories about the exhumation came forward.
They included a woman, a child herself in 1957, who said she had seen a man dragging Moira in Coatbridge, about 10 miles east of Glasgow. She picked a photograph of Gartshore out of a photo array.
Gartshore was convicted in 1957 of sexually assaulting a 17-year-old.
Sandra Brown, Gartshore's daughter, became convinced her father had killed Moira. She wrote a book after his death, "Where There Is Evil."
Graeme Pearson, a former deputy police commissioner in Strathclyde and now a member of the Scottish Parliament, suggested Gartshore should have been prosecuted years ago.
"It will remain a mystery why this man was not a significant suspect at the time of the missing person report and initial suspicion of a murder," he said.