The alleged unwanted sexual encounter happened in November. Wu had said that whatever occurred was consensual.
Democratic leaders had called for a House Ethics investigation after the initial reports of the allegation.
Wu said the well-being of his children should come first, so he will resign after Congress resolves the debate over the debt ceiling.
The woman reportedly decided not to press charges because there were no witnesses, and it would have been her word against Wu's.
The Associated Press contributed to this report.