He said he named his son after his grandfather Ben Allen in the social media post.
Cohen told his fans in December that he was an expecting his son. He announced the baby's gender on New Year's Eve and a baby shower was held, with some of "The Real Housewives" cast and singer John Mayer, CNN reported.
Related: TV personality Andy Cohen expecting first child via surrogate
He posted a photo of the Hollywood guests in attendance late last month.
Baby Benjamin was born Monday at 6:35 p.m. PT. He weighed 9 pounds, 2 ounces and was 20 inches long, People magazine reported.
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