In a post to Instagram on Friday 29 April, the Watch What Happens Live star said she was born in the early evening in New York City.
Her full name, Lucy Eve Cohen, was chosen in homage to his own parents, Lou and Evelyn Cohen.
In the picture, Cohen is seen smiling at the camera as he cradles the newborn against his chest.
“HERE’S LUCY!!!!! Meet my daughter, Lucy Eve Cohen! She’s 8 pounds 13 oz and was born at 5:13 pm in New York City!!!” he wrote.
“Her big brother can’t wait to meet her! Thank you to my rock star surrogate (ALL surrogates are rockstars, by the way) and everyone who helped make this miracle happen. I’m so happy.”
He also shared the picture on Twitter, writing that his “heart is bursting”.
Cohen already has a three-year-old named Benjamin, who was born in February 2019.
Well wishes for Lucy and Cohen have poured in on social media from celebrity friends.
“Congratulations! How wonderful and blessed is your family! May God bless you all!” Khloe Kardashian commented.
Actor Lisa Rinna wrote: “Omg congrats Andy! Welcome to the world Lucy! Everyone get up on a table and dance for Andy and Lucy now!”
“Hello sweet girl! Congrats Andy!”, said singer John Mayer, adding that he was already drawing up Lucy’s star chart.
Cohen previously hinted he was trying to expand his family in August last year. During an interview with E! News’ Daily Pop, he said he was “definitely open to it” and “would love to see it happen soon”.
“You know, I’m working on it. It turns out it takes a long time to make a baby,” he said.
Cohen, who also hosts Radio Andy on Sirius XM has spoken candidly about fatherhood in the past.
Two weeks after the birth of Benjamin, he told Today that he always knew he wanted children but wasn’t sure whether he would be able to.
“As a gay man, I never thought it was in the cards for me,” he said.
“There were points where I thought it was too late for me or that I was really focused on my career, and I was having too much fun to think about it.”
Sharing how his life changed following Benjamin’s arrival, such as his newfound early bedtime, Cohen said: “It’s not that easy for a single guy to do this on his own. It takes a village, as they say.
“I really wanted him, and the fact that he’s here and he’s so perfect and he’s in wonderful health…I have great gratitude for my surrogate and all the people who helped me get to this place.”