A lawyer for the city said Ferguson's insurance company had paid $1.5m (Â£1.2m).
Michael Brown Sr and Lesley McSpadden sued the city and police force for wrongful death compensation.
The judge called the sum "fair and reasonable for this wrongful death claim".
The city's insurance could have paid a maximum of $3m, according to the St Louis Post-Dispatch. The money will be split between the parents and their lawyers.
US District Judge E Richard Webber authorised the payment on Tuesday, but ordered the figure to be kept sealed.
"Disclosure of the terms of the settlement agreement could jeopardise the safety of individuals involved in this matter, whether as witnesses, parties, or investigator," the judge wrote.
He added that the figure "provides for a reasonable amount" for legal fees and expenses incurred by the family.
However, state law requires that the figure be released, leading to city attorney Apollo Carey's disclosure on Friday morning.
The lawsuit filed by the parents in 2014 claimed that their son's death was due to a police culture of pervasive hostility towards African-Americans, the St Louis Post-Dispatch reports.
They claimed Officer Darren Wilson used excessive and unreasonable force when he shot and killed Michael Brown on 9 August 2014.
The death led to riots and intermittent protests, and helped spawn the Black Lives Matter social justice movement.
A jury declined to indict Mr Wilson, who has since left the police force, after finding there was sufficient evidence to prove he had been attacked by Michael Brown.
The parents of Michael Brown, who was shot dead nearly three years ago by a police officer in Ferguson, Missouri, have received a financial settlement.