Peirce, a career criminal with a reputation for extreme violence, was shot dead as he sat in a car parked in Bay Street, Port Melbourne, on the night of May 1, 2002.
At the time, Supreme Court Justice Mark Weinberg said the convicted man, who cannot be named, played a significant role, knowing his job was to drive Veniamin to a location so he could execute Peirce.
“This was a brazen and callous crime … in a public street in the presence of bystanders,” he said.
A second man, accused of setting up the murder and luring Peirce to his place of death, was acquitted.
He cannot be named for legal reasons.
On Tuesday, the Victorian Court of Appeal rejected his application for leave to appeal his conviction.
The appeal judges ruled no miscarriage of justice had occurred during his trial and rejected all 12 grounds of appeal.
Peirce had been charged but was acquitted over involvement in the infamous 1988 Walsh Street police murders, in which young constables Steven Tynan and Damian Eyre were killed in an ambush.