O'Connor takes over the Rebels' chief playmaker role from fellow Wallabies back Kurtley Beale, who is sidelined with a broken hand, and will go head-to-head with Queensland Reds fly-half Cooper at the 'Stockade' in Melbourne.
Cooper was Australia's incumbent fly-half until he suffered a serious knee injury at the 2011 World Cup, and further problems with the knee last year saw Beale play the position for the Wallabies' final matches of last year's Rugby Championship and their season-ending tour of Europe.
O'Connor was ruled out of consideration altogether as he struggled with injuries in a forgettable 2012, but the talented 22-year-old previously played in the position for the Rebels and for the Wallabies during their 2011 northern hemisphere tour.
The relative merits of Beale, Cooper and O'Connor at fly-half have been hotly debated in Australia, but New Zealand-born Cooper has struggled to return to his mercurial best since coming back from his knee injury.
O'Connor, who has been playing at full-back in the Rebels' opening matches of the southern hemisphere competition, could steal a march on his rivals should he get the better of Cooper and with Beale expected to be sidelined for up to a month with a fractured right hand.
O'Connor will also captain the side for a second straight week after Welsh skipper and number eight Gareth Delve failed to recover from a shoulder injury, the Rebels said in a statement on Tuesday.
The British and Irish Lions play the Wallabies in three Tests in June and July.