Barry McGrory, 31, stabbed to death Scots Guardsman Paul McGee with a seven-inch blade he called his "baby".
Mr McGee died in his mother's arms after the attack outside the family's home in Lochwinnoch, Renfrewshire, in October 2009.
A jury returned a unanimous guilty verdict on McGrory following a retrial at the High Court in Glasgow.
Mr McGee's family and friends – including his mother Anne and sister Kelly – cheered loudly at the decision.
McGrory had originally been convicted two years ago but appeal judges later quashed the verdict. One of the points raised by the killer's lawyers was that a juror had been wearing a Help for Heroes wristband.
Judge John Beckett, QC, yesterday ordered the killer to serve a minimum of 20 years behind bars – the same jail term he received in 2010.
He said Mr McGee, 28, was a "brave and decent young man" .
Mr McGee's family made no comment as they left court.
The soldier was on leave at the time of the fatal attack on October 25, 2009. An Iraq war veteran, Mr McGee had been commended for bravery after trying to save a colleague whose armoured vehicle had slipped into a canal.
The family had been returning home in a taxi from a charity night when the incident occurred. Taxi driver John Banach spotted McGrory driving slowly with his fog lights on and flashed before overtaking.
The court heard this enraged McGrory and his passenger Ian Wallace, who chased after the taxi. When the vehicle stopped in McConnell Road, Lochwinnoch, Wallace confronted Mr Banach and attacked him.
Mr McGee stepped in before he and Wallace got into a scuffle.
As Mr McGee lay on the ground, McGrory went back to his car, grabbed a fishing knife and stabbed the soldier.
Mrs McGee told the court she found her son in the street. She said: "Neighbours came on to the street and told me he had been stabbed – then my son died in my arms."
She added: "He was a son every mum would have been proud to have."
It was the third time McGrory had stood trial for the murder of Mr McGee. His first conviction in 2010 was quashed on appeal on a number of grounds including that the judge misdirected the jury. Another appeal point was the fact one of the jurors was wearing a Help for Heroes wristband.
The second trial earlier this year had to be halted after an article in a local newspaper revealed McGrory was previously convicted of murder.
Before the start of the latest trial, Judge Beckett removed his Remembrance Day poppy and insisted other court staff should do the same in order to avoid bias claims.
Court staff were also asked not to wear any Help for Heroes badges or wristbands.
The jury heard McGrory – a takeaway delivery driver – had once again pinned the blame for the killing on Wallace.
He said: "I made mistakes that night, but I did not make the ultimate mistake and use the knife on that boy.
"Ian Wallace stabbed Paul McGee. Ian Wallace murdered Paul McGee."
Wallace had also originally been charged with murder, but the Crown dropped the case against him.
He instead pled guilty at the first trial to assaulting Mr McGee, the taxi driver and his girlfriend's mother Ann Laycock.
The jury was yesterday told McGrory had a previous conviction for assault and robbery and possession of a blade.
Judge Beckett said: "This was a horrifying assault with a knife that you called your baby.
"Paul McGee was a decent and brave young man who lost his life for no reason whatsoever. His only mistake was to seek to protect a taxi driver who was assaulted."
The judge also said McGrory had shown no remorse over the killing.
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