Cipriani, who has played seven Tests for England, was set to leave the team at the end of the season after signing a three-year deal with Sale Sharks last month.
The 24-year-old former Wasps player said via Twitter: "Going to be sad to leave all my team mates. Made some friends for life over here.. The back room staff at the rebels don't get enough praise.
"Loved my time in Melbourne @rebel-army and the fans having been truly amazing. So I thank u for all your support. Thank u."
Cipriani, the first England international to join an Australian Super Rugby team, had a troubled first year with Melbourne in 2011 and was sidelined for a month due to off-field disciplinary issues.
However, he appeared more settled this season, seemingly relishing his growing combination with Australia internationals James O'Connor and Kurtley Beale, although injury problems have prevented him earning a consistent run in the Rebels team.
He was retained for this season despite the arrival of star Wallabies backs James O'Connor and Kurtley Beale.
But even with O'Connor ruled out until June due to liver damage, the club have opted to pay out the remainder of Cipriani's contract, with eight rounds of the regular season remaining.
Although the Rebels are yet to release an official statement on the contract termination, a disciplinary breach is not believed to have been a factor.
Cipriani, who made 18 appearances during his two years in Melbourne, leaves with the Rebels fourth in the five-team Australian conference.
They are 13th of 15 teams in the overall standings, with two wins from eight attempts.
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