Monica Almeida/The New York Times

Kohlberg Kravis Roberts announced on Thursday that it had hired David H. Petraeus, a retired four-star general and former director of the Central Intelligence Agency, as chairman of the new KKR Global Institute.

The institute will focus on economic forecasts, communications, public policy and emerging markets. It will also help the firm’s portfolio companies expand globally, K.K.R. said. Mr. Petraeus’s team at the institute will include Ken Mehlman, the onetime chairman of the Republican National Committee, and Henry McVey, K.K.R.’s global head of macro and asset allocation.

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“With the addition of General Petraeus, we are building on the work we have done to understand the investment implications of public policy, macroeconomic, regulatory and technology trends globally,” Henry R. Kravis, co-chief and co-founder of the firm, said in a statement.

The announcement comes as Mr. Petraeus gradually re-enters the public sphere after an extramarital affair with his biographer, Paula Broadwell, led to his resignation as C.I.A. director.

It was an ignominious end to a government career that had a meteoric rise after the attacks of Sept. 11.

When he retired from the Army to lead the C.I.A. in 2011, Mr. Petraeus was possibly the most famous general of his generation. He commanded the American-led coalition during the troop “surge” in Iraq and later was the top military commander in Afghanistan. He also ran United States Central Command, responsible for all military operations in the Middle East, and helped lead the effort to draft the military’s field manual on counterinsurgency.

During a speech in California in April, Mr. Petraeus gave his first public remarks about the affair that forced him to leave government, expressing regret for the pain that the revelation had caused his friends, family and supporters.

Since then, the contours of Mr. Petraeus’s plan for post-C.I.A. life have emerged. In April, the City University of New York said he would serve as a visiting professor for one year.

More recently, however, Mr. Petraeus drew criticism for his role in developing the notorious “talking points” in the days after the September 2012 attack on the American diplomatic compound in Benghazi, Libya.

When the Obama administration this month disclosed a trove of e-mails sent among officials discussing the talking points, some expressed the belief that Mr. Petraeus had appeared overly concerned with protecting the C.I.A.’s image at the expense of the State Department.