The 29-year-old, who has been capped 37 times, would leave French Top 14 club Toulouse at the end of the current campaign to revive his career in Australia, the ARU statement said.
"I'm looking forward to getting home, seeing a few familiar faces and resuming my career in Australia," Burgess said in the statement.
"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 ongoing development of the game in Melbourne."
Burgess, who helped the Rebels reach the final of the now-defunct Australian Rugby Championship in 2007, made his last appearance for Australia at the 2011 Rugby World Cup finals.
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