Mehmet Ali Agca has been imprisoned in the Turkish city of Istanbul, since being extradited there in 2000 after spending 19 years in Italian jails.
He will be freed on parole on Thursday, his lawyer told the Associated Press.
Agca shot the pope in St Peter's Square as he was waving to crowds from an open car in 1981. The pontiff later visited him in jail and publicly forgave him.
The gunman was pardoned by the Italian authorities in 2000 and extradited to Turkey, where he was jailed for crimes unconnected to the papal shooting.
A Turkish court has now approved a prison document saying Agca has completed his term for those offences, the news agency Anatolia reports.
Mystery motive
Agca, now 48, was a 23-year-old known criminal with links to Turkish far-right paramilitaries at the time of the attack in Rome.
He fired several times at the late Pope John Paul II, leaving him with serious wounds to the abdomen and hand.
The critically wounded pontiff underwent emergency surgery - and, according to his own account, only just survived.
He met his attacker two years later in an Italian prison, when he publicly forgave him.
Vatican spokesman Joaquin Navarro-Valls said the Holy See would accept any ruling of the Turkish court over Agca's release.
He said the Vatican had only learned of the court's apparent decision from news reports and had not been given prior notice.
The motive for the attack remains a mystery, with Agca giving contradictory testimonies on his role and at times appearing deranged in court.
He was jailed in Turkey in 2000 for the 1979 murder of a left-wing Turkish journalist and two bank robberies.
There have been claims the attack in Rome was planned by the Soviet KGB and also involved the secret service of the former East Germany, the Stasi, and its Bulgarian counterpart.
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