When the crisis began, Geithner was president of the New York Federal Reserve, which helps oversee Wall Street. All told, he ran the New York Fed from 2003 until 2009.
Geithner, 52, left Washington in January 2013 and was succeeded by Jack Lew as Treasury chief. He first went to work at Treasury in 1988 and was later a top deputy to Treasury secretaries Robert Rubin and Larry Summers.
Reports surfaced after he left office that Geithner is writing a book about the financial crisis.
Warburg Pincus, established nearly 50 years ago, is a top player in private equity and manages $35 billion in assets.
In a deal this summer, Warburg sold eyecare specialist Bausch & Lomb to Valeant Pharmaceuticals for $8.7 billion. Years earlier, Warburg had led a private takeover of Bausch & Lomb.