"Nevertheless, the executive board noted that the incident was regrettable and reflected a serious error of judgment," the statement said.
Strauss-Kahn, 59, had admitted to an extramarital affair with Piroska Nagy, a Hungarian-born economist, but denied that he had harassed her and rejected suggestions she was given a more generous severance package than merited when she left the IMF in August.
Shakour Shaalan, the IMF executive director, also said that the board had unanimously accepted Strauss-Kahn's apologies and that it would continue to work with him.
"The mood of the board was very, very positive," Shaalan said after it met on Saturday to discuss the case.
"Our conclusion was that this in no way affects the effectiveness of the managing director.
"The managing director is very competent in carrying out his job. This was an unfortunate incident - the board has accepted his apologies."
Shaalan acknowledged that many in the IMF staff, especially women "are not at all happy" with Strauss-Kahn's behaviour.
"The managing director has expressed his regrets, I don't think that we can ask him to do more at this time," he said.
"We will continue to work with him. If there is some confidence that has been lost, he will regain it very soon."
But the scandal cast doubt within and outside the global institution on Strauss-Kahn's judgment, breaking just as the IMF confronts the world's deepest financial meltdown since the Great Depression of the 1930s.
In a statement, Strauss-Kahn said he had apologised to the board, IMF staff and his family for his behaviour.
"I agree with the statement made by the executive board today in concluding its inquiry," he said.
"I very much regret the incident and I accept responsibility for it."
Strauss-Kahn was appointed as head of the IMF in September 2007.