The announcement came after House Minority Leader Nancy Pelosi called for an House Ethics Committee investigation into Wu's conduct.
In a statement, Wu said he'll resign "upon the resolution of the debt-ceiling crisis."
Wu spokesman Erik Dorey told TPM that the Oregon Democrat "feels responsibility to see [the debt ceiling crisis] through."
"It's something that he's been speaking closely to his constituents about and feels its his duty to see through this important crisis," Dorey said.
"He's made it clear that anything that effects Medicare, Medicaid and Social Security are off the table," Dorey said. "He wants to continue to be an advocate of that position with his colleagues."
The Oregonian newspaper reported on Friday that a young woman who graduated from high school in 2010 left a "distraught" voice mail with Wu's Portland office which accused him of an unwanted sexual encounter in the fall. Wu previously disclosed mental health issues after his erratic behavior leading up to the 2010 elections.
Wu's full statement:
It has been the greatest privilege of my life to be a United States Congressman. Rare is the nation in which an immigrant child can become a national political figure. I thank God and my parents for the privilege of being an American.
Now, however, the time has come to hand on the privilege of high office. I cannot care for my family the way I wish while serving in Congress and fighting these very serious allegations.
The wellbeing of my children must come before anything else. With great sadness, I therefore intend to resign effective upon the resolution of the debt-ceiling crisis. This is the right decision for my family, the institution of the House, and my colleagues.
It is also the only correct decision to avoid any distraction from the important work at hand in Washington. I intend to go forward with new resolve and love of family, the State of Oregon, and our nation.