Mr. Greitens was indicted in February for a felony invasion of privacy charge after allegedly taking a nude photo of the hairdresser without her permission and transmitting it on an electronic device.
So it was stunning when he announced he was quitting with his mission incomplete.
"It's clear for the forces that oppose us there's no end in sight".
"I will walk off the battlefield with my held high", Greitens said.
Greitens said his resignation would take effect on Friday.
The incident reportedly occurred in March 2015 in the basement of his St. Louis home before Greitens launched his campaign for governor. The governor could also face other state or federal charges.
Eventually, the scandal also unspooled into a separate case looking into the illegal use of a charity donor list to raise campaign funds.
"This ordeal has been created to cause an incredible amount of strain on my family - millions of dollars of mounting legal bills, endless personal attacks created to cause maximum damage to family and friends", he said in a brief statement from his Jefferson City office, his voice breaking at times.
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"I am not ideal".
Mr Greitens said he had not broken any laws. She said "for whatever reason, I trusted him".
Roe said Greitens had been prepared for a two-stage fight. After being wounded in Iraq, he founded a veterans' charity and became a bestselling author and motivational speaker. He won an expensive Republican primary, then defeated Democratic Attorney General Chris Koster in the general election to give Republicans control of the governor's mansion for the first time in eight years. While Greitens enjoyed wide GOP majorities in the legislature he often clashed with lawmakers.
Greitens' affair became public on January 10, when St. Louis TV station KMOV aired portions of an audio recording secretly made by the woman's ex-husband in which she told him about her interaction with Greitens.
Gardner said at the time that she dropped the invasion of privacy charge after the judge in the case ruled that he would allow Greitens' attorneys to depose Gardner about whether she had knowledge of perjury committed by a private investigator hired by her office. She did not take questions after reading her statement. Those charges were later dropped. But, she says, details won't be released until Wednesday (5/30).
In the computer tampering case stemming from questionable fundraising activities, Greitens offered to leave office if Gardner would dismiss the charge, prosecutor's spokeswoman Susan Ryan said.
Greitens, a former Navy SEAL who was a political novice, attacked the investigations being conducted by prosecutors and the legislature over his alleged sexual misconduct during an extramarital affair and campaign finance abuses.
Investigators are looking into whether his campaign illegally co-ordinated with A New Missouri to hide donors by using shell companies to funnel money.