A former Wall Street investment banker with no public housing experience has been selected to lead the New York City Housing Authority, a sprawling bureaucracy struggling to overcome a financial crisis and a lingering controversy over elevator safety.

At City Hall on Wednesday, Mayor Michael R. Bloomberg introduced the agency’s new chairman, John B. Rhea, the former managing director of the Lehman Brothers global consumer retail group. He has also been an executive at JPMorgan Chase, where he completed more than $50 billion worth of transactions overseeing corporate finance as well as mergers and acquisitions, city officials said.

Such credentials, the mayor said, will help ensure the long-term fiscal stability of an agency that has a current operating budget deficit of $45.1 million. The city’s public housing system, the largest in the country, has been reeling in recent years from a lack of government financial support.

Among those critical of the mayor’s choice were five City Council members who said that at such a crucial time for the agency, a chairman with proven experience in affordable housing management was needed. They also expressed disappointment that council members were not consulted in the selection.