“Mareeh bin Ali bin Issa al-Asiri (Saudi national) practised witchcraft and sorcery, and was in possession of books and talismans from which he learnt to harm God’s worshippers and admitted adultery with two women,” said the statement.
The execution took place in the southern Najran province, SPA reported.
Human rights groups have repeatedly condemned executions for witchcraft in Saudi Arabia.
Last year the world’s top oil exporter, where judges follow the strict Wahhabi school of Islam and decide cases without reference to a written penal code, beheaded a man and a woman for witchcraft in two separate cases.
Mr Asiri was beheaded after his sentence was upheld by the country’s highest courts, the Saudi news agency website said.
No details were given of what he was found guilty of beyond the charges of witchcraft and sorcery.
Amnesty International says the country does not formally classify sorcery as a capital offence.
In 2010, a Lebanese television presenter of a popular fortune-telling programme was arrested while on pilgrimage to Saudi Arabia.
Though sentenced to death, after pressure from his government and human rights groups, he was freed by the Saudi Supreme Court, which that he had not harmed anyone.