Graham surprisingly resigned from his post with the Force earlier today despite still having two years left on his contract.
The former Queensland full back will see out the rest of the Super 15 season with his current club before taking over at the Reds at the start of the 2013 campaign.
Reds boss Ewen McKenzie, who was heavily linked with the Wallabies' job before Robbie Deans signed a new deal, will become director of coaching, with Graham becoming head coach of a side that includes the likes of Australia skipper James Horwill and star halfback duo Will Genia and Quade Cooper.
"The opportunity to return to Queensland with my family and coach my former team is something I couldn't pass up," said Graham, who represented the province between 1998 and 2002.
"I thoroughly enjoy and appreciate my time in Perth with the Western Force, and the experience I have gained over the past two years will make me a better coach for the next stage in my career.
"Purely from a personal standing as a career coach I felt it was something I needed to do but I wish to make it clear that it is in no way a reflection on Rugby Western Australia or the Force."
Graham previously worked with English Premiership sides Bath and Saracens and also enjoyed a stint as skills coach with the Wallabies between 2009 and 2010.
The 39-year-old, who took over from John Mitchell at the Force two seasons ago, will now look to register a famous double when the Lions head Down Under next year. Graham was part of the Australia A side that beat the 2001 Lions in Gosford, although he was forced out of that match after just 25 minutes when he was concussed by a tackle from Ben Cohen.
His decision to leave the Force earlier than expected has already prompted speculation as to who will replace him in the Garden City, with assistant coach Phil Blake thought to be an early front runner.
The Force intend to select an Australian coach if possible, with the likes of ex-Bath boss Steve Meehan and former Edinburgh coach Nick Scrivener expected to be among those who could also interest the Force.
"It is our preference to find an outstanding Australian coach either currently working overseas or in Australia to be Richard's replacement. However we will look at every possibility to recruit the best credentialed coach that is available in world rugby," said Rugby Western Australia's CEO Vern Reid.
"We are firmly of the view that the Head Coaching position at the Emirates Western Force is a prestigious role, not only in the Super Rugby competition but globally.
"From our initial discussions there has been strong interest from coaches with a world class pedigree and expect that now that the opening will be widely known we'll get plenty of enquiries."