The 32-year-old centre, who is currently sidelined with an ankle injury, may already have played his last game for the club as a result of the decision.
"I really just want to take this chance to say a massive thanks to Wasps for being so supportive and understanding of what has been a tough decision to leave," Flutey, who has made 81 appearances for the club across two spells, said.
A 14-cap international for the Red Rose, despite being born in Wairarapa, Flutey will head back down under ahead of his wife giving birth to their fourth child, before pursuing a career in Japan.
Flutey added: "Ultimately having four young kids away from family and a support network in New Zealand would be very tough.
"It goes without saying that the club will always have a huge place in my heart."
Flutey, who started his career with the Hurricanes, played for the British and Irish Lions in South Africa in 2009, becoming the first man to play for and against the representative side.