Mr Funke Kupper, who served as the chief executive of the ASX from October 2011, stepped down amid an investigation into his time at Tabcorp.
"The ASX board accepted that Elmer wanted to direct his full focus to the investigations which may be made into the Tabcorp matter," said ASX chairman Rick Holliday-Smith.
"Elmer has demonstrated leadership and energy during his time at ASX. He hands over a stronger team and a core franchise well positioned for future opportunities."
Mr Funke Kupper was the chief executive of Tabcorp in 2009 when a $200,000 payment was allegedly made to the family of Cambodian Prime Minister Hun Sen.
The payment came at a time when the company was attempting to gain an online gambling licence in the country, The Sydney Morning Herald reported.
Mr Holliday-Smith will assume the role of chief executive until a replacement is found.
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