The 29-year-old, who has been capped 37 times by Australia, is expected to be in contention for the British and Irish Lions' tour this summer.
He told reporters at a press conference: "Sometimes in life things are just meant to happen and I suppose I had always hoped that rugby would bring me back to Melbourne one day. Now it has, and I can't wait to pull on the Rebels colours again.
"My time in France has been great, but for me and the family it is time to come home. Super Rugby suits my playing style and so does the way the Rebels play."
Burgess will remain with the club for at least the next three seasons.