"We [are] thrilled to announce the arrival of [our] daughter Dakota -- #withloveandthanks -- AMEN," O'Donnell tweeted, alongside a photo of herself snuggling with Rounds and the infant.
People.com said the baby weighed 5 pounds, 5 ounces when she was born Jan. 5.
"Moms and baby are healthy and happy," O'Donnell's publicist said Wednesday.
O'Donnell and Rounds married last June.
The former chat-show host is also the mother of Vivienne, 10, Blake, 13, Chelsea, 15, and Parker, 17, with her ex-wife, Kelli Carpenter.