The former wicketkeeping great, 69, stepped down amid recriminations about the poorly performing team which crashed to a third-straight 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".
Marsh, one of several leading cricket officials under intense pressure, had previously insisted he would see out his contract which runs to the middle of next year.
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."
Australia's four-man selection panel now consists of Mark Waugh, Trevor Hohns and coach Darren Lehmann.
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 Proteas in Hobart this week.
Lehmann declared only four players -- captain Smith, David Warner, Mitchell Starc and Josh Hazlewood -- were sure to keep their places after Australia's second demoralising collapse in the Hobart Test.
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 former Test captain Ricky Ponting have been touted as possible successors.
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.
It has been a stormy series for the Australians, starting with a stunning first innings collapse of 10 for 86 in the first Test in Perth, when Australia squandered a 158-run opening stand to surrender meekly to the Proteas by 177 runs.
Critics pointed to other recent dark days in Australian cricket, including their demolition for 60 by England at Trent Bridge last year.
Australia now face being whitewashed in a home series for the first time in their history if they lose to the Proteas in Adelaide.
The last time they lost six straight Tests -- against India and England in 2013 -- the coach at the time, Mickey Arthur, was sacked.
Sutherland earlier Wednesday told reporters he would not be stepping down from his post as CA chief executive which he has held for 15 years.
Marsh, who replaced the previous chairman of selectors John Inverarity in May 2014, played 96 Tests from 1970-1984, taking a then-record of 355 dismissals as wicketkeeper.