In 2016 Vanunu was arrested and charged with violating three counts of his release conditions.
The Jerusalem Magistrate Court announced on Monday that Vanunu was cleared of two of those counts, one of which is related to an interview he gave to an Israeli television channel in 2015.
Vanunu denied that he posed a security risk and said that he only wanted to be free and join his wife, a Norwegian theology professor who lives in Oslo.
A sentencing hearing has been scheduled for mid-March, according to a court statement.
The conviction decision dates to mid-January, but was kept under wraps until Monday, an Israeli court spokesman said.
Vanunu began working at a secret Israeli nuclear facility at Dimona, a city in the Negev desert, in the 1970s. In the mid-1980s he leaked the inner workings of the Dimona plant to the Sunday Times newspaper, which published the photographs he had taken and exposed Israel's nuclear weapons program to the world.
The whistleblower, who converted from Judaism to Christianity in the 1980s, claims that Israel is particularly harsh on him due to his beliefs. Vanunu spent over 10 years of his original sentence in solitary confinement.