The Leeds-born singer, whose full name is Melanie Brown, cited “irreconcilable differences” in court documents published online.
The couple married in Las Vegas in June 2007 and have a five-year-old daughter, Madison.
Brown, 41, listed the date of separation as December 28, according to the papers filed with the Los Angeles Superior Court.
She is seeking joint custody of their daughter and has asked a judge to deny spousal support to film producer Belafonte.
Brown posted an Instagram photo of herself and Belafonte in February in which she described him as her “world”.
“We have been through everything that would normally tear couples apart and we have come out on the other side stronger,” she wrote.
Brown, who is a judge on the America’s Got Talent TV show alongside Simon Cowell, announced earlier this month that her father Martin had died aged 63 from multiple myeloma cancer.
As well as Madison, she has a nine-year-old daughter, Angel, from her brief relationship with actor Eddie Murphy, and an 18-year-old daughter, Phoenix, from her first marriage to dancer Jimmy Gulzar.
Belafonte also has another daughter, Giselle, from a previous relationship.