Ricardo Linton, 46, shot and killed Mohammed Basharat in the office of a taxi firm in Bradford, West Yorkshire, and attempted to murder a second driver, Jamshad Khan, in 2001.
Linton launched the attack in revenge for a road rage incident the previous day in which the wing mirror of his car was damaged.
He was found guilty by a jury at Bradford Crown Court in August, following a month-long trial.
Father-of-four Mr Basharat, 33, was hit by two bullets, in the head and mouth, and died at the scene, at the offices of Little Horton Private Hire.
The masked gunman then turned the illegal firearm on Mr Khan and pulled the trigger but the gun failed.
Sentencing Linton on Monday, Mr Justice Lavender said: “The killing of Mr Basharat was a targeted execution.”
He added: “You ended his life and brought life-long misery to his family.
“The pain will stay with them forever.”
The court heard that Linton had been convicted of possessing a handgun in the US in 1991 and, two years later, murdered a man by shooting him at “point blank range” in New York.
Mr Justice Lavender said: “That was another execution by you, eight years before you executed Mr Basharat.”
Linton left the US to avoid detection for the 1993 murder and entered the UK illegally under a false name.
He spent his time in the UK dealing crack cocaine in Bradford.
Mr Justice Lavender said Linton and Mr Basharat were involved in a fight near the taxi office on Park Lane the day before the murder, after the wing mirrors of their cars clipped each other.
He said Mr Basharat “got the better of” Linton, who left the scene saying: “You don’t know who you’re messing with. I’ll come back and get you.”
The judge said: “That threat to get Mr Basharat was carried out.
“That’s why he was killed – over a fight over a damaged wing mirror.”
Linton told the trial that he was not the gunman who killed Mr Basharat, but Mr Justice Lavender rejected that claim.
He said: “I am sure that you were the gunman. Your threat was that you would come back and get Mr Basharat.”
Linton vanished from Bradford on the day Mr Basharat was murdered and was later arrested in Jamaica in 2003 for the New York murder.
He was convicted of that killing in 2005 and sentenced to 25 years to life in prison.
On Monday, Mr Justice Lavender sentenced Linton to life with a minimum term of 31 years and 312 days for the murder of Mr Basharat.
He said the sentence means he will have spent a total of 50 years in prison since being arrested for the New York murder in 2003 and will be 77 before he is eligible for release.