Anthony McDonnell, 45, pleaded guilty to the manslaughter of postman Andrew Batten, who died following an assault in October 1995.
Police relaunched an appeal to find Mr Batten’s killer last month on the 20th anniversary of his death, issuing CCTV footage of the night in question.
McDonnell then handed himself into police on November 5 after police officers told his mother they were searching for him.
An earlier hearing at Leeds Magistrates’ Court heard that McDonnell and Mr Batten had become involved in an argument over a can of Coca Cola at a taxi rank.
It is believed Mr Batten was felled by a single punch that fractured his skull.
The father-of-four dressed smartly in a dark suit, black tie and wearing a striped purple tie looked stern-faced straight at the judge during the short hearing at Leeds Crown Court.
Richard Reed, representing McDonnell, asked for the case to be adjourned for a pre-sentence and psychiatric report to be compiled.
He said: “He doesn’t have a recent record of offending and attended himself at the police station.”
McDonnell, who was granted bail, will return to court on January 7 for sentencing.
Judge Tom Bayliss QC said: “You have pleaded guilty for an offence of manslaughter that occurred in 1995 where you unlawfully killed Andrew Batten. However I am going to grant you bail as it was before.
“The hurt you have caused by your actions is evident, You took a human life and you will be likely facing a lengthy prison sentence in my judgement.
“You must be under no illusions to what will be the likely sentence.”