The musician made the announcement on his website after the little girl was born on February 2.
Wainwright had the baby with Leonard Cohen's daughter Lorca and they will raise her along with Wainwright's partner Jorn Weisbrodt.
He said on his website: 'Darling daughter Viva Katherine Wainwright Cohen was born on February 2, 2011, in Los Angeles, California, to proud parents Lorca Cohen, Rufus Wainwright and Deputy Dad Jorn Weisbrodt.
'Lorca Cohen is the mother of the baby and Rufus Wainwright is the father. The little angel is evidently healthy, presumably happy and certainly very, very beautiful.
'Daddy 1 would like to offer everyone a digital cigar and welcome the little lady in with a French phrase from his favourite folk song, A La Claire Fontaine: 'Il y a longtemps que je t'aime, jamais je ne t'oublierai.'