Vanunu's wife, Kristin Joachimsen, told Norway's TV2 channel yesterday the couple requested family reunification after they wed in May 2015. It wasn't clear when he would relocate.
Joachimsen says: "Family values have prevailed."
Vanunu served 18 years in prison for leaking details and pictures of an alleged Israeli nuclear weapons programme to a British newspaper. He sought asylum in Norway after his 2004 release.
Israel then banned him from speaking with foreigners and leaving the country, among other restrictions.