Mr Strauss-Kahn apologised to his staff in a memo earlier
But the IMF board criticised Mr Strauss-Kahn’s “serious error of judgement” in the matter.
The managing director apologised this week for his brief liaison with IMF former senior economist Piroska Nagy.
The controversy comes as the IMF deals with the worst financial crisis since the Great Depression of the 1930s.
“The executive board noted that the incident was regrettable and reflected a serious error of judgment on the part of the managing director,” the IMF’s board of member countries said in a statement.
The board acknowledged that many female staff were unhappy about his behaviour, but found that Mr Strauss-Kahn’s affair with Ms Nagy – who worked in the IMF’s Africa department as a senior economist until she left in August – had been consensual.
In a statement to accompany the IMF board’s findings on Saturday, Mr Strauss-Kahn again apologised for his actions.
“I very much regret this incident and I accept responsibility for it,” he said.
“I have apologised for it to the board, to the staff of the IMF and to my family. I would also like to reiterate my apology to the staff member concerned for the distress this process has caused.”
The IMF chief’s wife, French television personality Anne Sinclair, said earlier that she and her husband had put what she called a “one-night stand” behind them.
Ms Nagy, a Hungarian-born economist, is now working for a bank in London.