The couple have named the little one, their second child together, Max Charles Murphy, who was born on November 30, USA Today reported.
According to a statement from Murphy's publicist, Max's middle name is a tribute to the actor's older brother and fellow comedian Charlie Murphy, who died of leukemia last year.
"Both mother and son are doing well," the statement read.
The 57-year-old actor and Butcher, 39, announced their pregnancy in August.
The couple, who have been in a relationship since 2012, already have daughter Izzy (two).
The "Dr Doolittle" star has oldest son, Eric, 29, with Paulette McNeely.
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