In July, the city reached agreement about the terms of the settlement with lawyers for a dozen current and former inmates who claimed to be victims of violence by correction officers.

The plaintiffs in the case, Nunez v. City of New York, received a significant boost last December, when Preet Bharara, the United States attorney for the Southern District of New York, joined a class-action suit brought by the Legal Aid Society as well as the law firms Emery Celli Brinckerhoff & Abady and Ropes & Gray. In August 2014, Mr. Bharara issued a scathing report documenting horrific treatment of teenagers at Rikers.

“For too long, a culture of violence has prevailed at Rikers Island, denying those within its walls the protections of the Constitution, rights to which all in this country, including prison inmates, are entitled,” Mr. Bharara said in a statement. “Through this agreement, we will remain vigilant in ensuring that reform at Rikers Island is enduring and enforceable.”

At the hearing on Wednesday, Celeste Koeleveld, a lawyer for the city, said that the agreement “dovetailed” with reform efforts already underway at Rikers. The city’s Correction Department, she said, had already begun putting many of the settlement’s provisions into effect.

“The department is prepared to hit the ground running,” Ms. Koeleveld said.

Central to the agreement is the treatment of teenagers at city jails. Last year, the administration of Mayor Bill de Blasio, a Democrat, pre-empted the settlement by doing away with solitary confinement for 16- and 17-year-old inmates. The correction commissioner, Joseph Ponte, has also vowed to eliminate solitary for everyone under age 22 by the end of the year.