"Sienna May Ivery, welcome to the world," the star wrote on her WhoSay account. "We love you more than words can say."
Ellen Pompeo and Chris Ivery have welcomed a second little girl into their family
Along with the message, Ellen also shared an adorable black-and-white photo of her beautiful baby girl receiving a big kiss from her proud daddy.
Little Sienna, who was born via surrogate, joins big sister Stella Luna, who recently celebrated her fifth birthday.
Her arrival was kept completely under wraps – much like Ellen and Chris' 2007 New York wedding.
Ellen Pompeo: 'Sienna May Ivery, welcome to the world'
Speaking to Australia's TV Week, Ellen said: "It's important to protect the privacy of the surrogate, but don't forget, I am the same girl who had the mayor of New York City marry me and it didn't get out for five days. I'm good at that!"
Becoming a parent has been particularly poignant for Ellen, given that she lost her own mother when she was just four years old.
"I try my absolute hardest every minute of the day to be the best mother I can to those children," she added. "And me not having a mother growing up, being a mother is more significant than I can put into words."