"Graeme worked with us during the recent ODI tour in the West Indies and we were really impressed with what he brought to the group.
"He is a very experienced player in all conditions and will bring a wealth of knowledge with him. "With an ICC Champions Trophy, an Ashes Series and an ICC World Cup all to be played in England in the near future, his knowledge of those conditions will also be invaluable."
Wisden Cricketer of the Year in 1987, Hick acted as assistant coach on the recent West Indies tour while Lehmann took a break.
"I have thoroughly enjoyed my current role with Cricket Australia and have worked with some great young up-and-coming players during my time," he said.
"To take the next step up with the men's team and getting the opportunity to work with some of the best players in the world is something I am really looking forward to."
The prolific Hick, who retired from first-class cricket in 2008 with 136 centuries and 41,112 first-class runs, was appointed batting coach through to 2020.
Cricket Australia said Greg Blewett would return to his job as fielding coach after filling in as batting coach following the departure of Michael di Venuto who moved to England to coach Surrey in March.
Australia will play five ODIs against South Africa starting from September 30.