Brown will also seek sole custody of Angel Iris Murphy Brown and reasonable child support, attorney Gloria Allred said at a press conference.
"I am here today for one reason and one reason only; her name is Angel," Brown said. "Angel is my baby and Eddie's. She will always know that she was planned and wanted by both of us."
Arnold Robinson, a spokesman for the 46-year-old actor, declined comment.
"We just don't comment on Eddie Murphy's personal life," he said.
Allred said in a statement that a DNA test has shown that Murphy is the father.
The statement said the test "established paternity but paternity has not been legally acknowledged."
Murphy has shown "shocking and appalling" conduct since the test, the statement said.
Brown, aka Scary Spice of the Spice Girls, dated Murphy last year.
The 32-year-old singer gave birth to her daughter April 3. She listed Murphy as the father on the birth certificate.
Murphy took the DNA test in June, Allred said.
Murphy has five children from his marriage to Nicole Mitchell Murphy, who filed for divorce in 2005.
Brown also has an 8-year-old daughter.
The Spice Girls recently reunited for a tour that is scheduled to begin later this year.