Larkham, who will be the Brumbies' head coach in 2023, had initially advocated for Rennie to be retained in his position but feels Jones is the right man to take Australia to the World Cup which kicks off in September.
"I had full trust they'd (Rennie and his assistants) get things together, but bringing someone like Eddie in is always going to be good for the program," Larkham told AAP.
"From the players' perspective there was probably a comfort level there with Dave. Everything's been shaken up and everyone will be on edge a bit… everyone knows Eddie's going to be watching those games.
"It adds a bit of spice into the mix."
Larkham played in 102 Tests for Australia between 1996 and 2007 and was the Wallabies' chief playmaker during their victorious World Cup campaign in Wales in 1999.
He also pulled the strings in Australia's backline when they finished as runners-up to England at the 2003 World Cup on with Jones in charge of the Wallabies during his first stint as their head coach.
Larkham has taken charge of the Brumbies where he has replaced Dan McKellar, who worked under Rennie as the Wallabies' forwards coach – a position which will now be reviewed.
"I'm a big fan of Eddie," Larkham said.
"I played under him and have been in contact ever since. I'm looking forward to sitting down with him and going through the program… (to) get some of that knowledge out of his head."