The stock and cash offer for the US lender is worth an estimated $14.6 billion and the definitive agreement will make Capital One one of the nation's ten largest banks.
Virginia-based Capital One is believed to be pushing forward with aggressive expansion plans in a bid to move beyond credit card lending and further into the US banking sector.
The boards of both groups have approved the deal, valued at $31.18 per North Fork share, and the resulting company will be the third largest retail depository institution in the New York region.
A statement from the companies said: "Capital One expects minimal disruption for North Fork's employees, customers, and communities since the companies have no geographically overlapping banking operations."
Under the terms of the acquisition agreement, North Fork chairman, president and chief executive officer, John A Kanas, will become the president of Capital One's banking business, reporting directly to Capital One chairman and chief executive officer, Richard D Fairbank, and will join Capital One's board of directors.
Mr Fairbank commented: "North Fork is a great strategic fit with Capital One and brings balance and diversification to our company. We're continuing to combine the power of national lending and local banking. North Fork provides us with a proven franchise and a strong growth platform in the largest banking market in America."