The kickbacks were disguised as consulting fees to a company run by Mr. Rivera’s son, which had “few if any business expenses,” according to court filings. Prosecutors said the elder Mr. Rivera used the money to make mortgage payments on his home.

“This unscrupulous real estate company owner resorted to bribes and kickbacks to become the landlord of choice for a taxpayer-funded nonprofit that provides vital homeless shelter services,” said Jocelyn E. Strauber, the commissioner of New York City’s Department of Investigation, which investigated the case with prosecutors from the U.S. attorney’s office in Manhattan.

Ms. Levin’s lawyer, Michael Farkas, declined to answer questions about the case, but he said in a statement that “this matter, and Ms. Levin’s conduct, are far more complex than suggested by the D.O.I. commissioner.”

As rates of homelessness have risen in New York, city officials have struggled to crack down on financial misconduct among some shelter contractors. Under a unique court order that requires the city to provide temporary housing to every homeless person, New York City farms out the operation of its shelters to dozens of nonprofit groups. In recent times, public spending on these groups has swelled to more than $2 billion a year.

Mr. Rivera helped found the Bronx Parent Housing Network in 2000 on a shoestring budget, and he expanded the organization into one of the largest operators of homeless shelters in New York City. His organization received more than $274 million in city money to run dozens of homeless housing sites from 2017 to 2021.

But as the money flowed in, Mr. Rivera found an opportunity to get rich: He collected an annual salary of $453,000, drove a Mercedes-Benz leased by the nonprofit and steered millions of dollars in contracts to friends and associates.

Ms. Levin, his partner in a separate housing venture, was one of those associates.

The Times investigation showed how Mr. Rivera’s organization paid millions of dollars in rent to Ms. Levin’s real estate company to lease two buildings for housing homeless people.

In court filings, federal prosecutors also detailed Mr. Rivera’s pay-to-play relationship with three contractors doing business with his organization. He arranged for a construction company, RJP Construction, to get contracting work in exchange for $66,000 in bribes, court filings show.

The construction company’s owner, Fernando Rodriguez, faced criminal charges for his role in the bribery scheme in March 2021 and pleaded guilty to these and other charges in a separate health care fraud case. In January, Mr. Rodriguez was sentenced to six months in prison and ordered to pay more than $66,000 in restitution to the Bronx Parent Housing Network.

Mr. Rivera also steered millions of dollars in contracts to a security firm, Prime Protective Bureau, in exchange for hundreds of thousands of dollars in kickbacks and a guarantee that the company would hire his former wife for a high-paying job. No one involved with the security company has been charged.

Prosecutors said the largest illicit payments to Mr. Rivera came from Ms. Levin’s company. The felony charge Ms. Levin pleaded guilty to carries a maximum prison term of 20 years, according to a Department of Investigation spokeswoman. Ms. Levin’s sentencing hearing is scheduled for July. As part of her plea, she agreed to forfeit more than $790,000 and pay restitution of more than $838,000 to the Bronx Parent Housing Network.