Geithner, who was president of the New York Fed at the outset of the financial crisis and has spent his life in the public sector, will take an active role in managing the firm.
Warburg's principals first approached Geithner with the idea this summer, the Wall Street Journal reported.
"When they approached me, they clearly wanted me to play a substantive role in helping them manage the firm," Geithner told the Journal.
At one point over the summer, Geithner had been seen as a possible replacement for Ben Bernanke as chairman of the Federal Reserve.
image: © U.S. Embassy New Delhi