Their representatives told People.com the couple exchanged vows in front of 25 friends and family on a beach on New Year's Day.
Edmonds wore a dress designed for her by Sugia Nazel and Jill Baracci and walked barefoot down the aisle to Gladys Knight's "Makings of You."
Murphy donned a cream suit and vest with an off-white handkerchief for the occasion.
The ceremony was followed by a private dinner and after-party where DJ Darrin Ebron from Los Angeles provided the entertainment, People.com said.
Edmonds and Murphy started dating last fall and were engaged in July.
The bride was previously married to Kenneth "Babyface" Edmonds, while the groom was previously married to Nicole Mitchell. Spice Girl Melanie Brown gave birth to Murphy's baby on April 3, 2007, nearly a year after his divorce from Mitchell was finalized.