"I got married three months ago to my wife who is in Norway," he told Israel's privately owned Channel 2 television station in what it said was his first-ever interview to Israeli media in Hebrew.
"She is the wage-earner, she is the one who is working, she can't live here," Vanunu said. "I want to start living my life."
The former nuclear technician was jailed in 1986 for disclosing the inner workings of Israel's Dimona nuclear plant to Britain's Sunday Times newspaper.
He spent more than 10 of his 18 years in prison in solitary confinement.
In Friday's interview he said that after years of working at Dimona and winning promotion he was not searched on entry and was able to smuggle in a camera and take 58 pictures of the facilities without being detected.
"I've finished with all that," he told the channel. "I don't have any secrets and I want to leave. They should let me leave and live my life with my wife abroad."
He married Norwegian theology professor Kristin Joachimsen at a Lutheran church in Jerusalem on May 19th.
Vanunu, 60, converted to Christianity shortly before being snatched in Rome by Mossad agents and smuggled to Israel.
Released in 2004, he was jailed again for 11 weeks in 2010 for breaking the terms of his release by meeting a foreigner, a prison official said.
In 2011 the High Court barred him from emigrating on the grounds that he still poses a threat to state security.
He is barred from speaking to journalists but has repeatedly given interviews to foreign media, while shunning the Israeli press.
Channel 2 said that its interview was cleared for broadcast with the military censor.
Israel is the Middle East's sole if undeclared nuclear power, refusing to confirm or deny that it has such weapons.
It has refused to sign the nuclear Non-Proliferation Treaty or to allow international surveillance of the Dimona plant in the Negev desert of southern Israel.