Jones was sentenced to death in 2002 for killing Paul Howell during a carjacking three years earlier. He maintains his innocence. Photo: AFP / Oklahoma Department of Corrections
Kevin Stitt said he was commuting the sentence to life imprisonment without parole.
Hundreds of students earlier walked out of school demanding clemency for Jones.
Jones was sentenced to death in 2002 for killing Paul Howell during a carjacking three years earlier. He maintains his innocence.
His case has attracted the support of celebrities including reality TV star Kim Kardashian and anti-death penalty activists.
Jones' execution by lethal injection was scheduled for 4pm local time at the state penitentiary in McAlester.
But Gov Stitt, a Republican, said he intervened "after prayerful consideration and reviewing materials presented by all sides of this case".
The state's Pardon and Parole Board earlier recommended in a 3-1 majority vote that Jones' sentence be commuted to life in prison with the possibility of parole.
The case has attracted widespread attention in recent years, partly due to the 2018 ABC documentary series The Last Defense.
More than six million people signed a Justice for Julius petition which states he was put on death row because of "fundamental breakdowns in the system tasked with deciding".
Jones was found guilty of fatally shooting Howell, an insurance executive, during a 1999 carjacking on his driveway.
In October, he was among five people who won stays of execution from a three-judge panel of the 10th Circuit US Court of Appeal.
"I did not kill Mr Howell," he wrote in a letter to the parole board in April, after exhausting his appeals.
"I did not participate in any way in his murder; and the first time I saw him was on television when his death was reported."
Howell's relatives have said Jones' calls for clemency have victimised them further.
- BBC