NEW YORK — The federal government seized more control over the New York City Housing Authority on Thursday, reaching an agreement with the city intended to correct years of mismanagement that prosecutors said had exposed hundreds of thousands of residents to lead paint and other health hazards.

The settlement meant Mayor Bill de Blasio avoided a complete management takeover of the city’s housing authority, home to more than 400,000 low-income New Yorkers.

But as part of the deal, the mayor accepted the appointment of a powerful federal monitor and committed the city to spending $2.2 billion over the next decade to repair the authority’s dilapidated buildings.

The agreement also will lead to the replacement of the authority’s interim chairman, Stanley Brezenoff, whom the mayor brought in last year to steer NYCHA after a lead paint scandal and the departure of the authority’s chairwoman.

Ben Carson, the Housing and Urban Development secretary, said the monitor, who will be paid by the city, would be named in a couple of weeks. One candidate said to be under consideration is Bart M. Schwartz, a former senior prosecutor under Rudy Giuliani when he was the U.S. attorney. Schwartz is now chairman of Guidepost Solutions, a security firm.

The deal comes two months after a judge overturned an earlier settlement and consent decree that was reached last year.

As part of the new deal, the city would agree to invest an additional $1 billion in the authority’s dilapidated housing stock over the next four years and $200 million per year after that, the same commitment it had made in the earlier settlement that was rejected, the officials said.

Under the deal, Carson did not commit to provide additional money for NYCHA. Since 2001, NYCHA has seen its federal funding cut by more than $2.7 billion.

The deal establishes deadlines for NYCHA to remediate five hazards detailed in the government’s lawsuit last year — lead paint, mold, pest infestations, heating failures and inadequate elevators.

The agreement calls for the immediate remediation of lead paint in apartments with children under 6 years old and, over two decades, the complete abatement of all lead paint in NYCHA developments.

Since 2012, a total of 1,160 children under 18 living in public housing have been found to have elevated lead levels in their blood.

This article originally appeared in The New York Times.