Cohen made the announcement on Instagram Monday alongside a photo of herself holding her newborn while in a hospital bed. Hart Violet's face is covered up with a heart image.
"We're so in love. Hart Violet Braun," Cohen captioned the image.
Braun reposted Cohen's photo and wrote a tribute to his wife and daughter whom he says arrived eight days late on Saturday.
"Welcome to the party Hart Violet Braun! Daddy will always be here! And mommy...Mommy is a rockstar!! We love you! #sheownsme," he said.
Braun and Cohen are also parents to Jagger Joseph, 3 and Levi Magnus, 2.