Abdullah bin Fandi al-Shammari was executed in the northern town of Hael, the agency said.
Shammari was 23 when he was arrested and jailed for beating to death Moojab bin Mohammed al-Rashidi after a row.
His trial dragged on for five years and at the time the court set him free and ordered him to pay the victim's family "blood money" after ruling Rashidi's death was involuntary homicide.
But Rashidi's family demanded an re-trial and Shammari was re-arrested, tried and sentenced to death in 1983.
He lingered on death row however because under Saudi law, the sons of the victim had to come of age and each one had to decide whether or not to accept the "blood money".
Rashidi's sons insisted the death sentence should be carried out.
Tuesday's execution brings to 10 the number of people beheaded in Saudi Arabia so far this year.
In 2012, the ultra-conservative Muslim kingdom beheaded 76 people, according to an AFP tally based on official figures. The US-based Human Rights Watch put the number at 69.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia's strict version of sharia, or Islamic law.