Petraeus will lead a new institute created by the fund and specializing in economic and geopolitical forecasts, public policy and emerging markets, the company said, confirming an earlier report by the Wall Street Journal.
KKR, which has specialized in taking over large listed companies, hopes to cash in on Petraeus's contacts and experience to assess potential acquisitions, the paper quoted its sources as saying.
Since leaving the CIA, Petraeus, 60, has said he planned to teach at the University of Southern California and City University of New York.
Petraeus, a hero of the Iraq war and former commander of allied forces in Afghanistan, became CIA director in 2011. He was one of the most decorated and respected military people of his generation.
He resigned November 9, 2012 after admitting an affair with his biographer Paula Broadwell, 20 years his junior.