Cooley has been involved in winning Ashes campaigns for both sides
Australia could be without a specialist bowling coach when the Ashes starts in November after farming out Troy Cooley to their Centre of Excellence.
Cooley, one of the masterminds behind England's 2005 Ashes success, defected to his native Australia to help Ricky Ponting's men to the 2006-07 whitewash.
He remained Australia's bowling coach when England won the Ashes in 2009.
But he now takes Greg Chappell's role to head up the Brisbane facility that has replaced the Australia academy.
Chappell, the former Australian captain, has moved to the newly-created role of national talent manager, based in Melbourne.
Cricket Australia's acting chief executive Michael Brown said: "Troy will continue to support the Australian team throughout the Ashes Test series and the World Cup campaign."
But a CA statement also suggested it might need someone to take over his day-to-day position before the first Ashes Test begins on 25 November.
It read: "CA will be working to replace Troy as pace-bowling coach as soon as practicable after further discussions with [head coach] Tim Nielsen and an assessment of current needs in this area."
Cooley, 44, made his name during the 2005 Ashes campaign, when he was credited with helping Andrew Flintoff and Simon Jones master reverse swing and confound the Australian batsmen.
The following year he was snapped up by the Australians after failing to reach agreement with the England and Wales Cricket Board on a new contract. The ECB later faced a deluge of criticism about losing his services to their greatest rivals.
England will be coached by Andy Flower in Australia, with Graham Gooch assisting the batsmen, David Saker the fast bowlers and Mushtaq Ahmed working with the spinners.