The 36 year old gave birth last Monday but the famous couple only revealed the news on Saturday evening during an appearance on an American chat show, The Late Show with Stephen Colbert.
New dad Bobby, who has been in a relationship with Rose for three years, told the studio audience; 'I had a baby on Monday, yes.'
Exciting baby news for Bridesmaids star Rose, who gave birth to her first child last week!
The former Will and Grace actor explained that he had been 'comfort eating' to cope with the strain and exhaustion of having a newborn in the house.
The 45 year old, who has also starred in HBO drama Boardwalk Empire, said; 'You know, I didn't do anything. We [fathers] don't do anything and I'm so tired. I think I've gained 28 pounds since Monday.
'I mean, I'm not kidding you. Like, this jacket fit so well, like, last Thursday. But I've been eating so much.'
Bobby, who already has a 20-year-old son with ex-wife Jenny Lumet, also announced the new baby's name - Rocco.
When quizzed by host Stephen Colbert about whether their choice was after Saint Rocco, Bobby confessed that lack of sleep had given him the famous 'baby brain'.
'Actually, yeah, patron saint of the sick... pretty sure. Could be wrong. I'm tired.'
But just in case the situation seemed a little too realistic for new parents, Bobby reminded us of his celebrity status by sharing some of the gifts the family has received since the news broke.
Hollywood legend Al Pacino even sent baby Rocco a personalised gift.
Rose's pregnancy was kept under wraps until November last year, but entering her third trimester she was unable to keep her bump covered.
The couple live together in Brooklyn, New York, but had kept their love out of the spotlight for several years until Bobby called the actress the 'love of my life' during the 2013 Emmy awards.
While accepting his award for Outstanding Support Actor, Bobby told the audience about their previously secret relationship.
Rose previously dated Australian actor Brendan Cowell for six years before splitting in 2010.