In a statement, Mr Strauss-Kahn, 62, said he had already informed the executive board of his intention to step down “with immediate effect”.
He again firmly denied the criminal charges against him.
Mr Strauss-Kahn – who is being held in New York’s Rikers Island prison – is expected to make a new plea for bail.
In the statement, Mr Strauss-Kahn said: “It is with infinite sadness that I feel compelled today to present to the Executive Board my resignation from my post of Managing Director of the IMF.
“I think at this time first of my wife – whom I love more than anything – of my children, of my family, of my friends. I think also of my colleagues at the Fund; together we have accomplished such great things over the last three years and more.
“To all, I want to say that I deny with the greatest possible firmness all of the allegations that have been made against me.
“I want to protect this institution which I have served with honour and devotion, and especially – especially – I want to devote all my strength, all my time, and all my energy to proving my innocence.”
The IMF said it would release information “in the near future” about the appointment of Mr Strauss-Kahn’s successor.
The organisation’s deputy, John Lipsky, has been in interim control of the IMF since Mr Strauss-Kahn’s arrest on Saturday.
Bail hearing
Mr Strauss-Kahn faces a number of charges in connection with the alleged sexual assault of a 32-year-old maid in New York’s Sofitel hotel on 14 May.
They are: committing a criminal sexual act, attempted rape, sexual abuse, unlawful imprisonment and forcible touching.
Police have removed a piece of carpet from the Sofitel hotel, in search of evidence to support the maid’s allegation she was forced into an act of oral sex.
Mr Strauss-Kahn’s lawyer, Benjamin Brafman, said on Monday that the defence believes the forensic evidence “will not be consistent with a forcible encounter”.
On Monday a judge in New York denied Mr Strauss-Kahn bail – despite the offer of a $1m (£618,000) guarantee – saying there was a risk the IMF chief would flee the country.
However, he will make a new plea for bail at a court hearing on Thursday morning, Mr Brafman says.
The BBC’s Laura Trevelyan in New York says the defence will offer a new package that they hope will convince the judge that Mr Strauss-Kahn will not try to flee while he prepares his defence.
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