Browder was a 16-year-old sophomore when he was accused of stealing a backpack and arrested, later charged with second-degree robbery. He was released in 2013, when charges against him were dropped.
Browder just turned 22 when he hanged himself in 2015.
The New York City Law Department confirmed the settlement of the family's civil suit.
"The family believes settlement is fair and reasonable," Browder family attorney Sanford Rubenstein said at a news conference Friday. "But they hope that his memory will be honored with the reforms that still have to take place within our prison system."
While at Rikers, he attempted suicide at least six times, according to a Browder lawsuit filed against New York City, its police department, the Bronx district attorney and others, including several correction officers. The suit claims he was falsely arrested, maliciously prosecuted and denied a quick trial.
Browder was hospitalized for five days in November 2013 after attempting suicide. According to his attorney, he attended a community college in the Bronx and had a GPA of 3.5.
Browder's former attorney, Paul Prestia, told CNN in 2015 that Browder was bright, humble and someone with a great sense of humor.
"Before going to jail, I never had any mental illnesses," Browder told HLN. "I never tried to hurt myself, I never tried to kill myself, I never had any thoughts like that. I had stressful times before going to jail, but not like during jail. That was the worst experience that I ever went through in my whole life. "
"Years on the end of near-total isolation is a terrible price," Kennedy wrote.
CNN's Sophie Tatum and Ariane de Vogue contributed to this report.