"After much consideration and discussion, we have jointly decided that we will forgo having a legal ceremony as it is not necessary to define our relationship further," Murphy's representative said in a statement issued to TMZ.com.
"While the recent symbolic union in Bora Bora was representative of our deep love, friendship and respect that we have for one another on a spiritual level, we have decided to remain friends."
The Hollywood actor and his movie producer bride exchanged vows in front of 25 friends and family during a sunset ceremony on a beach New Year's Day.
Murphy and Edmonds 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.