The Grey's Anatomy actress, 44, and husband Chris Ivery recently welcomed baby daughter Sienna May Ivery, who will join 5-year-old big sister Stella.
"Sienna May Ivery, welcome to the world," Pompeo tweeted. "We love you more than words can say."
Pompeo later expressed her gratitude to her co-workers, tweeting, "Sienna was born via surrogate & I would like to thank my whole @ShondalandTV family for helping us enjoy these first few weeks privately."
This news follows Pompeo's announcement that she could soon be transitioning to a behind-the-camera role.
"I definitely don't have a strong desire to act after Grey's," Pompeo said at BuzzFeed Brews with Facebook Live last month. "I feel myself transitioning. I don't find acting terribly empowering. For the place I am in my life ... I don't necessarily want to work for other people."
Pompeo started a production company called Calamity Jane, and seems to be leaning more towards producing.
"Producing is very challenging, but it's very interesting to me and fun to try and find projects," said Pompeo. "That's where I really have fun now. That's fun for me, to find a book or an article or an idea and turn it into something."