In a Facebook post governor Ahn Hee-jung "begged forgiveness" for his "foolish behaviour" and said denials issued by his office were untrue.
Kim Ji-eun, who said she was inspired by the #MeToo movement, accused him of raping her four times in eight months.
The #MeToo campaign has slowly began to gain traction in South Korea.
"I apologise to everyone, especially Ms Kim Ji-eun," said Mr Ahn. "Everything is my fault. As of today I will resign...[and] stop all my political activities."
The police are currently investigating the allegations of sexual assault, which Mr Ahn has neither explicitly admitted to nor denied.
Mr Ahn, the governor of South Chungcheong province, was a political heavyweight.
He ran against current President Moon Jae-in to be the Democratic Party of Korea's nominee for the 2017 presidential elections. Though he lost, he was widely seen as a leading candidate to replace Mr Moon in the 2022 elections.
On Monday night, Ms Kim appeared in an interview broadcast by local television network JTBC, where she made her allegations against Mr Ahn public.
She accused the 54-year-old of raping her four times over the course of eight months, from June 2017 to February this year, and said he had sexually harassed her on many occasions.
She also alleged there were other victims.
Mr Ahn's office had initially claimed that he had consensual sex with Ms Kim.
"Our sexual relations were not consensual, and I'm sure he knows it. I was not in a position where I could say no," said Ms Kim in the interview, as reported by the Korea Times.
Mr Ahn, who is married, said in his later statement that his office had "falsely" announced that the relationship was consensual.
Ms Kim said the #MeToo campaign, sparked by the widespread allegations of sexual abuse in Hollywood, had given her the courage to come forward.
"After the movement came into the spotlight, Mr Ahn appeared to be anxious," said Ms Kim in the interview, as reported by the Korea Times. "On 25 February he called me into his office and apologised. But then, he did it again."
The campaign, which has seen thousands using the hashtag to share their experiences of sexual harassment, has spread across the globe.
It was slow to take off in South Korea, but recently gained ground after a number of women came forward.
'Betrayed and shocked'
People South Korea have been expressing their disappointment at the news about Mr Ahn.
"I don't know what to do. I [feel] betrayed and shocked," said one user on Facebook. "I thought he was a good politician."
"I believed in you and supported you. You've taken my support, turned it into power and used it to control someone else," another user added.
"I thought you could be the one who could lead our country after Mr Moon. I can't believe it. I'm speechless," said one user.
"Kim Ji-eun, thank you for your courage. We will cheer you on," one commented.
More about: SouthKorea