James McGowan, 57, was sentenced to a minimum of 18 years for stabbing Owen Brannigan to death in Coatbridge, North Lanarkshire in 1999.
He had denied the attack, which took place after McGowan returned from Australia for his mother's funeral.
The jury was told how in 2012 he told a helpline he had killed a man.
Mr Brannigan had been married to McGowan's sister Carol, but they divorced in 1984
McGowan emigrated to Australia with his wife in 1980.
A trial at the High Court in Edinburgh was told there had remained bad feeling between McGowan's family and the 47-year-old victim.
Judge Lady Scott said he was guilty of a "brutal and cowardly" attack.
She said: "You took it upon yourself on a brief return for your mother's funeral to seek out Mr Brannigan and murder him in a pre-meditated act of revenge."
After the stabbing, McGowan then returned to Australia earlier than planned.
In 2012, McGowan called a helpline and said something was "slowly eating away" at him.
He said: "Once you've crossed the line and you jump back... you know you can always go across the line.
"Some people can't go across it and I know I went and done it and it's a frightening thing - a frightening thing to deal with.
"You go 'Jesus, I can't kill people. But I did.'"
He was later extradited from Australia to face trial.
The case was one of the first to be investigated by the Crown Office in Scotland's cold case unit.
McGowan's son Ryan was in court to watch his father be sentenced.
The pair exchanged brief smiles as McGowan was led handcuffed to the cells.
Ryan played for Hearts from 2008 to 2013.
The Australia international also had spells with Dundee United, Ayr United and Partick Thistle, and last played for Chinese club Henan Jianye.
The father of former Hearts footballer Ryan McGowan has been jailed for life for the murder of his former brother-in-law.