The Australian Broadcasting Corp. said Leanne, 13, was found dead in 1991 near her Goodna home, which is west of Brisbane.
ABC said Leanne's older sister's former boyfriend, Stafford, was been in prison for 15 years, even though his conviction was quashed in 2009.
Although Queensland Police Commissioner Ian Stewart said investigators have identified new evidence that links Stafford to the crime, the prosecutors have decided against proceeding.
"The Queensland Police Service respects his decision that there is no public interest in retrying the case," Stewart said.
Both Stafford and the investigator who worked to clear his name, Graeme Crowley, said police have not considered any other suspects.
"I'm obviously a bit disappointed that they've spent all that time, and supposedly all that effort, and come up with no evidence to suggest anyone's responsible," Stafford said.