The former wicketkeeping great, 69, stepped down amid recriminations about the poorly performing team which crashed to a first-ever home series defeat to South Africa on Tuesday.
"This is my own decision and no one within Cricket Australia has pressured me or even suggested that I should do this," Marsh said in a statement.
Cricket Australia said it would hold an extraordinary meeting later Wednesday to decide on an interim replacement, with an announcement "in due course".
But on Wednesday he said it was time for a new perspective after a run of defeats which has prompted severe criticism in Australian media.
"Clearly, 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," Marsh said.
"I have always had the best interests of Australian cricket foremost in my heart, and that's why I have made this decision."
The panel has been under heavy scrutiny over the shocking results of Steve Smith's national team, culminating in their latest batting collapse of eight for 32 in their innings and 80 runs defeat to the Proteast in Hobart this week.
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.
Australia's team announcement for next week's third and final day-night Test in Adelaide has been delayed until Sunday so selectors can assess players' form in domestic Sheffield Shield matches.
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