Todd Gloria, the Democratic City Council president, becomes acting mayor until a special election is held within 90 days after the resignation takes effect.
"For my own part in causing all this, I offer my deep apology," said Filner in city council chambers after the resignation was announced. "The city should not have been put through this, and my own personal failures were responsible."
Filner apologized to the city council as well as to the city and his former fiancee. He also said the media fed the "hysteria" and created a "monster." He went on to cite a series of progressive achievements and ongoing trends in the city he wants to see continue.
"To all the woman that I offended: I had no intention to be offensive, to violate any physical or emotional space," said Filner. "I was trying to establish personal relationships. But the combination of awkwardness and hubris I think led to behavior that many found offensive.
"I again as I have in the past sincerely apologize to all of you and I will try to make amends in any suitable manner."
The San Diego City Council met behind closed doors for about 90 minutes after hearing public comment over a possible settlement with the mayor.
Under the settlement, Filner will not receive a buyout or pension. The city will provide a joint legal defense with Filner for sexual harassment claims, but only those filed by past or present city employees or others doing city work. The city can seek reimbursement from Filner for any damages that might be awarded. If Filner hires a private attorney, the city will pay up to $98,000 of his legal expenses.
San Diego's city attorney, city leaders and the mayor's attorneys announced Wednesday that a proposed resolution was reached following three days of mediation.
The mayor's former communication's director, Irene McCormack Jackson, was the first to go public and is the only one to file a lawsuit against Filner and the city.
Attorney Gloria Allred represents McCormack Jackson in her suit against Filner, which has not been settled. Allred and her client are thankful the mayor has finally agreed to resign.
"I think the mayor saw the handwriting on the wall, and the handwriting said, 'Bob, it's time to go,'" said Allred.
Sixteen women have accused the 70-year-old mayor of inappropriate behavior.
Filner had resisted numerous calls to resign. He apologized for what he called a failure to respect women, but denied the allegations of sexual harassment.
We're also learning of more possible legal troubles for Filner. The state attorney general's office confirms there is a criminal investigation underway but will not release any of those details.
Shortly after 3 p.m. PT, the Democratic National Committee announced it approved a resolution calling on Filner to resign. The DNC is meeting in Scottsdale, Ariz.
The Associated Press and City News Service contributed to this report.