The former Test wicketkeeper had intended to step down in mid-2017 but announced he was vacating the role immediately.
"This is my own decision and no-one within Cricket Australia has pressured me or even suggested that I should do this," said Marsh in a media release.
"Clearly, though, it is time for some fresh thinking, just as it is for our Test team to welcome some new faces as we build for the future.
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“I have always had the best interests of Australian cricket foremost in my heart, and that's why I have made this decision."
The statement added: “I have thoroughly enjoyed the role and want to thank the coach, the staff, my co-selectors and all the players for their support and honesty over the past two and a half years. It was a thrill for me to be involved in many successes, including the World Cup win in 2015.
“I wish the captain, coach and the team all the best going forward. We will be great again.’’
Australia's four-man selection panel now consists of Mark Waugh, Trevor Hohns and coach Darren Lehmann.
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Only hours before Marsh's announcement, Cricket Australia chief James Sutherland voiced support for him to see out his contract.
"He said he will finish up June and we will make decisions about where and how we transition to that in the future," Sutherland told reporters in Hobart.
Former Test fast-bowler Jason Gillespie and Test captain Ricky Ponting have been touted as possible successors.
The board will hold an extraordinary meeting later on Wednesday, where a decision on an interim appointment is expected to be reached.
(With input from AFP and Cricket Australia's media release)
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