Head Coach Gareth Jenkins rang the Scarlets hooker to talk through his options and the pair, together with Rees's expectant wife Becky, came up with the plan to use him for one game only.
"It was a difficult one when Gareth called me and everyone's priority is that I'm there for the birth," said Rees, who celebrated his first wedding anniversary last month.
"This will be our first child and although I love playing for my country, it's obvious that I simply have to be there.
"The plan to fly me back gives me the best of both worlds. I've been on the phone to Becky everyday and the midwife tells us things are on course, so hopefully the plan will come off."
Rees will name a daughter Brooke or a son either Cory or Cole and he says all his dreams could come true at once if he can seal victory over the Wallabies before returning home to his soon-to-be larger family.
"The game will be tough and I'm going to have to work a little harder to focus," he said. "But I want to hold my hand up for a World Cup spot and knowing that I only have the one game on tour means that I can put all my energy into those eighty minutes of rugby.
"I'm really looking forward to it and I have Gareth and the management team to thank for making it possible for me."