Democratic leaders had called for a House Ethics investigation after the initial reports of the allegation. Wu had said that whatever occurred was consensual.
Wu said Tuesday the well-being of his children should come first, so he will resign after Congress resolves the debate over the debt ceiling.
Wu, 56, has won seven terms. In 2004, he won despite acknowledging a decades-old college incident in which he tried to force a former girlfriend to have sex. Voters said they disliked an opponent’s attempt to use that against Wu as part of a political campaign.