They claim Mel has cited “irreconcilable differences” as the reason for the split.
The former ‘X Factor’ judge, who is based in the US, has also listed listed “joint custody” in the filing, in relation to responsibility of the couple’s five-year-old daughter, Madison.
The papers also reveal Mel is being represented by top family law attorney Susan Wiesner, who has worked with a number of US stars.
Reports of the couple’s split were first broken by American magazine People, with the Daily Mail later publishing copies of the legal papers.
HuffPost UK has also contacted a representative for Mel for further comment.
Mel and Stephen first tied the knot in Las Vegas in 2007 after a five-month romance, later renewing their vows in front of their families in Egypt in 2008.
The couple have denied rumours of a split various times over the years, while the latest claims come just six weeks after Mel made a public declaration of love on social media.
Posting a photo of the two of them together on Instagram, she wrote: “My baby boo @stephenthinks11. We have been through everything that would normally tear couples apart and we have come out on the other side stronger. You loved me before I even [knew] how to really love myself. You are my world, honey.”
Mel was previously married to Spice Girls dancer Jimmy Gulzar, with whom she has 18-year-old daughter Phoenix.
When the couple divorced in 2000 after two years of marriage, Mel later went on to have a relationship with actor Eddie Murphy, also having a child, Angel, together.
Stephen also has another daughter, 12-year-old Giselle, from his previous relationship with Nicole Contreras.
News of her split also comes just two weeks after the death of her father, Martin Brown, who passed away following a five-year battle with cancer earlier this month.
Mel reunited with her estranged sister Danielle to be at his bedside in his final moments, posting a photo of them both holding his hand on Instagram.
“Both of us his children were by his side and would like to say thank you to St Gemma’s and all the doctors and nurses for there amazing care and support over the years,” she wrote.