"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.
"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.
"I have always had the best interests of Australian cricket foremost in my heart, and that's why I have made this decision.
"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."
CA chief executive James Sutherland, national coach Darren Lehmann and team high-performance manager Pat Howard had all recently expressed their support for Marsh to see out his tenure.
Sutherland sent a firm message on Wednesday morning that Marsh was going nowhere after Australia's dismal innings-and-80-run loss to South Africa at Bellerive.
"Rod's ... like everyone else - they're doing the best job they can and working very hard at it," Sutherland said.
"He's said that he's going to finish up in June and we'll make decisions about that and how we transition that in the future."
Sutherland met Marsh in Hobart after Wednesday's media conference but only learned of his desire to step down on returning to Melbourne.
Howard had previously suggested he wouldn't contemplate Marsh's potential successor until January, but that would become his top priority.
Ricky Ponting and Steve Waugh have been floated as potential candidates but both former skippers have busy schedules and might not be willing and able to sign up for what is a full-time job.
Waugh and Hohns will be watching Sheffield Shield matches that start on Thursday, with the squad for the third Test against South Africa expected to be named on Sunday.
The Proteas hold an unassailable 2-0 lead in the three-Test series.
- AAP