The French season ends on June 1, meaning he could be considered for the Rebels' clash with Britain and Ireland's elite at AAMI Park on June 25.
Burgess is highly unlikely to be considered for the Wallabies in the three-Test series with the Lions but a provincial outing against Warren Gatland's troops is now a distinct possibility.
"I'm looking forward to getting home, seeing a few familiar faces and resuming my career in Australia," said Burgess after signing a two-and-a-half-year deal with the Rebels and the Australian Rugby Union.
"The rugby has been different in France, especially in terms of the physicality on a weekly basis - the games can be a real grind - but it's been a great learning curve that I've had.
"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.
"The 2006 Rebels was one of the happiest rugby experiences of my career. 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. So I know that we are going to do some very good things together.
"Obviously representing my country again is a goal, but I'm also looking forward to linking up with the Rebels and playing my part in the on-going development of the game in Melbourne."
Burgess left Australia for Europe after the 2011 World Cup and hasn't represented his country since then.
He is likely to be in the mix for this year's Rugby Championship, however, given that he was the primary back up to Will Genia prior to his departure.
His switch to Melbourne, whom he helped reach the 2007 final of the now-defunct Australian Rugby Championship prior to their Super Rugby birth, will see him represent his third Aussie franchise.
Burgess began his career at the Brumbies but moved to the Waratahs after failing to unseat the legendary George Grean from the No9 position in Canberra.
He won't be free to play for his new side in this year's Super Rugby competition, though, unless there is an injury to one of the existing Rebels halfbacks Nick Phipps or Nic Stirzaker.