“With sport in Australia planning to return soon, making the change now will also allow Dave to begin his new role as head coach of the Australian national team,” Bombrys said.
“We are grateful to Dave for everything he has done for our club over the past three seasons, and particularly for how he has been supportive of the current situation, as well as his willingness to share his vast coaching knowledge with all of our coaches.”
Rennie has been in contact with his Wallabies assistants and RA for months but is clear now to direct all his energy towards reviving the stocks of the national team.
It is unclear when Rennie and wife Stephanie will travel to Australia, although reports in Scottish media suggest he will depart at the earliest opportunity.
They will likely face two weeks in isolation upon arrival in Sydney.
Former Chiefs coach Rennie led Glasgow to the final four of the Pro14 in his two full seasons in charge.
They reached the quarter-finals of the European Champions Cup last year but narrowly missed out on the last eight this season.
Scottish Rugby chief executive Mark Dodson said Rennie’s tenure had been a success.
“He has brought on a young, exciting group of players at Glasgow over that period, reached a Pro14 final and led his coaching group at the club superbly.”