The 33-year-old will move to Australia after helping Chiefs win the Premiership title for the first time by beating Wasps 23-20.
He is expected to have a spell in Japan with an as yet unnamed Top League side before joining Melbourne in January.
Parling won 29 England caps and also played three Tests for the British and Irish Lions in Australia in 2013.
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"I'm excited about the opportunity to test myself in the Southern Hemisphere," he said.
"Hopefully I can add value to the Rebels, and help the team continue the great growth and profile of rugby in Victoria."
Parling began his career with Newcastle Falcons, and also had a six-year spell with Leicester Tigers where he won two Premiership titles, before joining Exeter in 2015.
"Geoff's signing is a strategic recruitment for the club as we look to evolve our squad and program for 2018 and beyond," Rebels chief executive Baden Stephenson told the club website.
"Geoff boasts a wealth of international and domestic experience in successful rugby programs so he will contribute to the strong leadership at the club, along with his world class lineout skills and hard running qualities which will complement our squad."

1 June 2017 Last updated at 12:50 BST
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His side's 20-16 victory ended a run of seven consecutive defeats for the Welsh region and seven wins in a row for Connacht.
It was only the third home league match of the season for Blues, and Wilson hopes it can lead to improved form.
"Hopefully it's given us a springboard to build some confidence," he said.
"I'm relieved after the last seven minutes of that game, but pleased with a big effort form the players to beat the league leaders."
Wilson believes the lack of home games has been a factor in the Blues' poor start to the Pro12 season.
"It's only our third home game of the season and people forget that and we've had two wins at home and a loss to Glasgow.
"We've talked about building that home record and if we are ever to give ourselves a chance to get where we want to be we have got to be winning at home."
The Blues' Cardiff Arms Park ground was out of commission during the Rugby World Cup when it was used as a fanzone.
It meant the Blues playing five of their opening seven Pro12 matches away from home - and losing all of them.
The former Wales Under-20 coach says it is important for his players to bond around the victory.
"I want the boys to have a beer and get that winning feeling back," he added.
"Winning pulls the squad together.
"It's not coming to work on a Monday on the back of another loss because that can get negative.
"We can gel from this win - pull together and get close and enjoy it. When you get the win you cherish it and build on it."
Exeter Chiefs lock Geoff Parling has signed to play for Super Rugby side Melbourne Rebels for the 2018 season.
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There's a general election coming up on 8 June, when adults will vote to decide who will run the UK.
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Cardiff Blues' win over Pro12 leaders Connacht can act as a springboard for the rest of the season, according to head coach Danny Wilson.