New York State has agreed to hire a monitor and a research expert to serve as watchdogs of the New York City foster care system to settle a federal class-action lawsuit that alleges foster children are enduring irreparable harm after lingering too long without permanent families.

Advocates for foster children had found that children in the city spent twice as much time in the foster system as others in the rest of the country. The suit, filed in July against the state and city child welfare agencies, was brought by the public advocate, Letitia James; Marcia Robinson Lowry, executive director of A Better Childhood, an advocacy group; and lawyers from Cravath, Swaine & Moore.

The settlement, signed on Tuesday, was a partial victory. The state’s Office of Children and Family Services, which oversees the city’s Administration for Children’s Services, has agreed to a series of reforms. But the city has not settled.

“Perhaps this will compel A.C.S. to come to the table,” Ms. James said in an interview.

City officials had pointed to improvements. By June 2014, the number of foster children in the system had dropped to around 11,000, about a fifth of the number in the 1980s, and their time in the system had also been reduced.

Ishanee Parikh, a spokeswoman for Mayor Bill de Blasio, a Democrat, said that the city agency was already addressing issues raised by the settlement.

On Tuesday, Gov. Andrew M. Cuomo, a Democrat, said he was “proud that we are taking action,” and that the plaintiffs deserved praise “for drawing attention to the issue.”

Under a consent decree, the state and its child services agency denied any wrongdoing but agreed that a monitor would assess the systemic issues affecting the placement of foster children into permanent homes.

The monitor, who will be in place for at least three years, will also keep track of any mistreatment of foster children. The research expert, who will be retained for at least two years, will conduct yearly reviews of case records for compliance.