John Mackie was given a life sentence for bludgeoning Mike Mosey to death with his own baton.
The former Merseyside officer whispered his murderer's name to his son as he lay fatally injured in a pool of blood.
Mackie was found guilty at the High Court in Glasgow of killing Mr Mosey at his home on 12 or 13 August last year.
The jury took just 45 minutes to return a unanimous guilty verdict.
Judge Lord Hardie told Mackie, 33, that he must serve at least 18 years before he is eligible for parole.
Sentencing Mackie, Lord Hardie said: "This was a frenzied and unprovoked attack upon a vulnerable man. It will be for the parole board to decide when, if ever, you are released.
"It is clear Mr Mosey was a useful member of society and had given public service.
"In later years he had certain difficulties and certain members of the community where you live, including you, took advantage of him sponging off him."
The last words of Mr Mosey, 58, helped convict Mackie.
The court heard that Daniel Mosey, 29, went to his father's house at Carnwath Road, Braehead, near Forth, Lanarkshire, after receiving a 2am mobile phone call during which he heard only the sounds of moaning and dogs barking.
His son said: "When I went into the kitchen I saw my dad lying there on his face. There was blood everywhere.
"I bent down, put my hands on his shoulder. He asked who was there and I said, 'Dad, it's Daniel' and he moaned and rolled back on to his front.
"I asked him, 'Dad, who's done this to you?'
"It was then he named Mackie - saying he had 'kicked the s*** out of him'.
He added: "I'll never forget his words as long as I live. I phoned my sister Rachael , held the phone near dad's mouth, and asked him to repeat the killer's name.
"For the second time he named Mackie. Dad never spoke again, but thankfully his dying words helped to convict this evil man."
Mackie, who was represented by Donald Findlay QC, denied murdering Mr Mosey claiming he had hit him once with the baton and then left. He said the killing must have been carried out by someone else.
Mr Mosey was in a coma on a life support machine for nine days. His family were at his bedside when he died.
Mackie's attack with the truncheon left Mr Mackie with a fractured skull and horrific brain injuries.
A pathologist said that Mr Mosey had been struck seven times and the court heard that the force of the blows broke the baton.
The victim's son added: "It was an awful way to go for a man who was loved by his family and helped the community so much.
"He was a police officer in Liverpool, but only for a few years, and when he left his mates signed the truncheon that was to kill him and gave it to him.
"It was one of his treasured possessions which he jokingly called 'Mr T'."
Daniel Mosey revealed that his father had ferried blood supplies and transplant organs from hospital to hospital for a charity organisation.
But after Mr Mosey's wife Frances died in 2005 he turned to drink.
His son added: "Dad fell in with a bunch of men, including Mackie, who sponged off him. "Things began to go missing from the house, and it was frequently broken into. For his own protection he looked out 'Mr T' and hung it on the wall ."