"I want to feel free, I'm not free here," said the 50-year-old Vanunu, who on release was subjected to a series of sweeping restrictions, including a ban on travelling abroad as well as holding unauthorised meetings with foreigners.
"The only way to feel and enjoy freedom and start my new life as a free human being will be when I can leave Israel and live my life in the US, in Europe or in London," he said.
Vanunu was sentenced in 1986 to 18 years in prison for "treason" and "espionage" after leaking top-secret details about the Dimona nuclear plant, where he was employed, to The Sunday Times.
"I tried to inform the world and to try to stop this nuclear proliferation," he said on Sunday in the live television interview with BBC's Breakfast with (David) Frost programme.
"My hope was that by revealing the nuclear secrets I would bring new states towards real peace in the Middle East and the abolition of nuclear weapons in all the Middle East," he said.