A federal judge on Tuesday approved a settlement in the lawsuit brought by the family of Michael Brown against the police officer who fatally shot him in Ferguson, Mo., ending the legal chapter of a case that sparked national outrage over the police’s treatment of black people.

Mr. Brown, who was 18 and black, was unarmed when he was shot three years ago by Officer Darren Wilson, who said that Mr. Brown had attacked him and charged toward him when he fired the fatal shots. Some witnesses said that Mr. Brown had his hands up, but both federal and state prosecutors questioned that narrative and determined that there was not enough evidence to charge Mr. Wilson, who is white, criminally.

Judge E. Richard Webber of the Eastern District of Missouri sealed the details of the settlement, which also named the city of Ferguson and the former police chief, Thomas Jackson. The amount would be less than $3 million, according to a person familiar with the details of the case, who spoke on the condition of anonymity because no one is allowed to speak about the particulars of the case. Three million dollars is the most the city can pay under its insurance, according to The St. Louis Post-Dispatch.

The lawsuit was filed by Mr. Brown’s father, Michael Sr., and his mother, Lesley McSpadden.

“I hope that this gives the family some closure and I hope they feel like this gives them a little bit of justice,” said Emily Davis, a Ferguson resident who has advocated police reform. “But I do not feel like the community has justice yet. People’s experiences with the police and the court system are not changing quickly. The city is still not changing openly and willingly.”