Mr Elliott, who is currently ANZ's chief financial officer, will become the chief executive of ANZ on 1 January 2016.
Mike Smith will step down after eight years as chief executive officer and as a director on 31 December 2015.
In a statement, ANZ chairman David Gonski said Mr Smith had transformed ANZ into Australia’s "only international bank with a focus on Asia Pacific".
"Mike was appointed chief executive as the world was entering the global financial crisis. Despite those headwinds and a volatile environment for banks around the world, his leadership has seen ANZ continue to grow market share in Australia and establish a strong, growing New Zealand business under one brand," Mr Gonski said.
"He has transformed ANZ into one of Asia Pacific’s leading banks with operations in 34 countries, delivering strong outcomes for our customers and for our shareholders."
Mr Gonski said Mr Elliott was the "outstanding candidate for the role of chief executive".
"Today’s announcement is a result of a detailed review of external and internal candidates. Shayne’s international banking and financial experience, together with his background in Australia and New Zealand makes him the right person to lead ANZ in a challenging global environment," Mr Gonski said.
Mr Elliott said he was "honoured" to have the opportunity to lead ANZ.
"ANZ is a bank that plays an important role supporting our customers and communities in 34 countries. Our people are guided by a clear strategy and a strong set of values. I look forward to working with Mike during the transition period and to building on the foundation he has established," Mr Elliott said.
Mr Smith said: "Our succession process saw a smooth transition to our new chairman last year and now is the appropriate time for me to step down.
"Shayne and I have worked closely together for the last six years, particularly in his last three years as CFO. I know he will make an exceptional chief executive."
