White, who decided to return to South Africa in September after missing out on the Australia coaching job, raised the Brumbies from the Super Rugby doldrums and turned them into championship contenders in two years in charge.
Fisher, an assistant coach when the Brumbies won their two Super Rugby titles in 2001 and 2004 and under White, as well as head coach from 2005 to 2008, will be director of rugby.
Larkham, who won 102 caps for the Wallabies and was a World Cup winner in 1999, steps up from his position as backs coach to take his first head coaching role at the franchise he represented 116 times on the pitch.
"I'm very privileged and certainly very honoured to have been given this opportunity, Larkham said.
"We have a great group of players at the moment and I'm looking forward to developing the team alongside Laurie.
"Laurie and I have worked extremely well together over the last two years. This new structure allows us to continue to deliver our coaching on the field, whilst sharing responsibility off it."
Under White, the Brumbies developed a squad of some depth with no shortage of quality. Six of Australia's starting line up for Saturday's Test against England at Twickenham play their Super Rugby in Canberra, including captain Ben Mowen.