The couple also shared vlogs to their personal YouTube accounts explaining that they'd been looking at rental properties for a couple of months.
"This has been a long time coming, we've been wanting to tell you guys for ages but we were like 'We have to hold off and try and make it a surprise.' Finally it's out so we're super excited," Anna said in her video.
Meanwhile, Josh's vlog showed what moving day was like and how they spent their first night with limited furniture.
"Gonna indulge in a fat Dominoes pizza and a red wine because that is deserved as well," Josh said at the end of the moving day vlog.
In a chat with Now To Love right after their big win on the reality dating show, Josh and Anna confessed they were keen to have their own love nest together.
Sydney boy Josh added that he'd be keen to move interstate but originally suggested moving to Queensland where it would be neutral turf for the couple.
"I've lived in Sydney my whole life and you can definitely get stuck on the Northern Beaches," he explained. "But for me, if I was to move and Anna agrees, we both want to have a fresh start together so we were thinking the Gold Coast would be perfect for us. A new change, we don't know that many people up there and it'll be new for us both."
Despite the fact Love Island brought Anna and Josh together, there have been some clues that indicate the show will not return for a third season.
According to The Daily Telegraph's Confidential, Love Island is yet to be renewed by the Nine Network after season two suffered consistently low ratings last year.
Although, in a statement reportedly provided to the publication, a Nine spokesperson said no official announcements have been made.
“We haven’t made any announcements about Love Island. Sophie is a much loved part of the Nine family,” they said.