Mr Hodges is currently chief executive of New Zealand and managing director of ANZ National Bank, a role he has held since late 2005.
He will now be responsible for driving the group's operational performance and managing key client and other external relationships, ANZ said.
Mr Hodges was formerly group managing director of ANZ corporate, and has previously been the bank's chief economist.
Mr Edgar had been with the bank for 25 years.
"Bob has had an outstanding career at ANZ and his leadership and track record over many years has established him as one of Australia's leading banker,'' ANZ chief executive Mike Smith said in a statement.
"I know Bob intends to continue his involvement in the business world and I want to extend my personal thanks for his invaluable contribution to ANZ and wish him every success.''
Meanwhile, ANZ also said Jenny Fagg will join ANZ's management board following her appointment to the role of chief executive New Zealand and managing director ANZ National, replacing Mr Hodges.
Dr Fagg is currently deputy chief executive officer of ANZ National and managing director of retail distribution.
She was previously managing director of Consumer Finance for ANZ in Australia.
People in Business
Share market has strong opening
M. Tangredi Restaurants’ executive indicted on charges of fraud
Boral to separate cement operations
