The 26-year-old has recovered from a troublesome foot injury to line up at AAMI Park against the Brumbies, who are the top-ranked Australian team.
The Rebels, meanwhile, have had a disappointing start to their season with losses in each of their three outings.
Sydney-born Kellaway had a breakout Wallabies season last year, making his debut in the victorious France series in July and was selected in all but one of the Wallabies' 14 Tests during the international season.
As well as winning Rugby Australia's rookie of the year award he was nominated for 2021 World Rugby breakthrough player of the year.
Kellaway said it was an easy decision to extend his deal with Melbourne.
"It's been a whirlwind 10 months for me personally, and I'm extremely grateful for the opportunity the Rebels gave me to return to Super Rugby last season and really excited about what we can achieve together in the future," he said.
"I feel like Melbourne is home for me now and I'm looking forward to adding as much value as I can both on and off the field over the next three years.
Wallabies coach Dave Rennie was happy to have Kellaway commit, particularly after losing winger Marika Koroibete to Japanese rugby.Â
"Andrew's a top man and a mature rugby player who has quickly become an important member of our mob on and off the field," Rennie said.
"His journey to becoming a Wallaby is well documented and a new contract is reward for his self-belief, determination and hard work.
"We all saw the impact he was able to have in his first year at Test level and his work ethic and professionalism will ensure he continues to put himself in the best position to do that moving forward."
