While NYCHA’s residents are living with lead, this guy’s raking in the gold.

The New York City Housing Authority’s federally imposed watchdog is charging cash-strapped City Hall nearly $600 an hour, according to a five-year contract arranged behind closed doors with the feds, new documents show.

Bart Schwartz, a former federal prosector who’s now chairman of contractor Guidepost Solutions, stands to personally make

$1.2 million a year — or even much more — under the terms of the deal.

When asked about his salary, a rep for Schwartz called his pay “deeply discounted.”

But residents of the Big Apple’s housing developments expressed outrage, given the poor conditions under which they’re living.

“It’s bulls–t. It’s ridiculous,” Marie Joyner, 58, who has lived at the Queensbridge Houses since 1996, told The Post. “The knobs on my bathtub have been there since this damn place was built. I asked for new knobs and they say they have none. But they have $600 [an hour] to pay this man? It’s a waste.”

For the first year of the deal, Schwartz’s earnings are capped at $350,000, according to the 13-page contract Guidepost Solutions signed earlier this year with City Hall.

But once the cap is lifted, the former Giuliani-era Manhattan federal prosecutor could take home up to $1.2 million a year if he works eight-hour days at his $594-an-hour rate.

Meanwhile, NYCHA faces an astounding $38 billion repair bill for public housing — and City Hall’s own math shows it has come up with only $24 billion so far.

A spokesman for Schwartz said the chairman was focused on achieving “decent, safe sanitary living conditions for NYCHA residents” and had visited more than 200 developments.

“The scale and complexity of the problem he’s helping solve is unprecedented in the history of monitorships, public or private,” said the spokesman, Montieth Illing­worth. “Despite that challenge, he’s limited his total fees and deeply discounted his hourly rate, fees that the city approved and which the city, not NYCHA, pays.”

But City Council Speaker ­Corey Johnson said Schwartz’s salary seemed very high.

“That’s a huge salary and we need every dollar we can to go towards critical repairs of deteriorating housing stock,” he told The Post.

“I do think the monitor plays an important role and this was put in via consent decree in the settlement with HUD [the US Department of Housing and Urban Development] so that’s important. But the amount of money for the amount of time seems like way too much at this point.”

According to the nonprofit news Web site The City, Schwartz initially asked for $20 million a year for the total cost of his firm’s work, including his salary. He was eventually haggled down to $12 million by the city for the first year, though there was little detail on how that money will be spent.

There’s no cap on what Schwartz can spend over the next four years of the contract, the documents reveal.

Schwartz’s executive officers are also getting paid $503 an hour under the deal, while investigators can make as much as $366 an hour. Even the clerical staff can bill as much as $137 an hour.

His firm’s overall fee far exceeds what other federal monitors in New York are paid, according to city data.

In their first year, the FDNY’s diversity monitor charged $1.03 million, the Department of Correction $1.7 million and the NYPD stop-and-frisk monitor $2 million.

After a bombshell lawsuit brought by the Manhattan US Attorney’s Office in June 2018, City Hall, NYCHA and HUD agreed to appoint an outside monitor to keep the agency in check, amounting to a partial fed takeover of the agency.

The suit alleged that NYCHA officials lied for years about conducting mandated lead checks in apartments and mounted an organized effort to cover up crumbling living conditions.

But interim NYCHA chair Stanley Brezenoff expressed doubts about the arrangement, fearing a monitor would become overbearing, and walked.

In February, without city input, the feds hired Schwartz to oversee the embattled Housing Authority, the city’s biggest landlord, which provides homes to more than 400,000 New Yorkers.

Since February, Schwartz’s monitorship has published two of its promised quarterly reports that exposed continuing problems and mismanagement at the agency.

However, the watchdog operated for months without disclosing the size of its own budget and without its contract becoming public.

City Hall repeatedly rejected Freedom of Information Law requests from The Post and other news organizations seeking the documents and referred questions to federal authorities, who declined to comment.

E-mails later obtained by The City show that City Hall’s own lawyers were iced out of discussions among Schwartz, HUD and the Manhattan US Attorney’s Office over Guidepost’s budget — even though city taxpayers are ­legally required to pay the bills.

Schwartz’s spokesman said taxpayers actually got a “discounted” price.

Schwartz is a former federal prosecutor who worked in the 1980s with then-Manhattan US Attorney Rudy Giuliani as head of his criminal-prosecutions division.

But, he is new to the public-housing arena and tasked with providing oversight of the nation’s biggest such agency, which faces daunting challenges.

While Schwartz is making big bucks, the city is already paying current NYCHA chair Gregory Russ $403,000 a year.

City Hall rolled out its NYCHA 2.0 plan to fund $24 billion in repairs in December, but that outlay may prove inadequate.

The de Blasio administration has struggled to get a key piece of the program off of the ground, potentially increasing the shortfall.

“While prior administrations turned their backs on residents, we rolled up our sleeves and made a historic investment to turn around NYCHA with our federal partners,” said City Hall spokeswoman Olivia Lapeyrolerie. “NYCHA’s new leadership team will continue to work closely with the monitor to improve the lives of the 400,000 New Yorkers who call NYCHA home.”

Additional reporting by Ebony Bowden