Cooper, who will make his professional boxing debut in February, has been shrouded in controversy after publicly declaring the Wallabies had become a “toxic environment”.
He was fined 60,000 Australian dollars and later rejected an incentive-based contract with the ARU last month before finally agreeing to terms.
The 24-year-old said: “It’s no secret that I have a strong passion and desire to represent Queensland and Australia. I love playing for the Reds and the Wallabies.
“It’s a great feeling to know things are sorted and now I can continue to improve as a player and as a member of the Reds and the Wallabies.
“I’m confident I’ll front for round one in peak physical condition and primed to play the best rugby in my career.”
Acting ARU chief executive Matt Carroll added: “This means Quade Cooper and the Reds can now focus entirely on the upcoming 2013 Super Rugby season.
“Quade can now look forward to getting back on the field next year and playing for the Reds and in turn stake his claim for re-selection in the Qantas Wallabies squad.
“Next year is an exciting year for Australian Rugby with the British and Irish Lions venturing to our shores for the first time since 2001.”
Reds director of coaching Ewen McKenzie is looking forward to having Cooper and Will Genia, who recently signed a new deal, in the halves next season.
“We have been preparing as if Quade and Will were both going to be around next season, so nothing much changes in that respect,” McKenzie said.
“Obviously we’re targeting winning the championship next year, so it will be good to push on with our preparations without the peripheral noise.