Christopher Lee, a married 46-year-old with one son, was elected in 2008.
In a statement on his website, he said he regretted harming his family, staff and constituents, adding: "I deeply and sincerely apologise to them all."
Republicans gained control of the House of Representatives in the November mid-term elections.
"The challenges we face in western New York and across the country are too serious for me to allow this distraction to continue, and so I am announcing that I have resigned my seat in Congress effective immediately," Mr Lee said.
Representative Chris Lee of New York
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