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.
"It's a great feeling to know that things are sorted and now I can continue to improve as a player and as a member of the Queensland 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."
"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."
"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.
"Even some of our Wallabies have started to filter back into the set up this week, so it's good for our environment and culture. We're all working towards 2013."