In June 1990, Buntion fatally shot Houston Police Officer James Irby, 37, during a traffic check.
At the Texas State Penitentiary in Huntsville, the world's oldest death row inmate was killed by lethal injection.
Carl Wayne Buntion, 78, was the state's oldest murderer awaiting death.
On Thursday night, April 21, he was pronounced dead.
In June 1990, Buntion fatally shot Houston Police Officer James Irby, 37, during a traffic check.
Buntion, who was riding in the passenger seat at the time, shot Irby in the head while he spoke with the driver.
The 78-year-old, who already had a long criminal history, attempted to flee the scene during the traffic stop but was forced to return by the officer.
According to witnesses in a neighbouring automobile, he then opened fire on Irby and another cop, killing Irby and wounded the second officer.
He then fled on foot, only to be apprehended and convicted of capital murder and sentenced to death the following year.
He hasn't admitted to shooting and killing Irby, but claims it was in self-defense.
Buntion was questioned by KHOU11 only days before his execution, and he told the station that he has regretted the murder "every day for the previous 32 years."
"If Mrs Irby was sitting right there, I'd tell her the same thing: 'I'm sorry it occurred,'" he continued. Every day, my heart breaks for her and her children.
"Perhaps by executing me, they'll finally be able to put this behind them."