October 02, 2014 05:15 PM

Kevin Mazur/Getty

Surprise! Ellen Pompeo is a mom once more.

On Thursday, the Grey’s Anatomy star, 44, revealed she and husband Chris Ivery welcomed their second daughter about two months ago.

Sienna May Ivery welcome to the world. We love you more than words can say,” she captioned a black-and-white Instagram photo of the new dad sweetly kissing their daughter.

The family’s new bundle of joy arrived with the help of a surrogate and joins big sister Stella Luna, 5.

“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,” Pompeo jokes to Australia’s TV Week. “I’m good at that!”

Who helped Pompeo keep little Sienna’s arrival a secret? None other than producer Shonda Rhimes, the queen of Thursday night TV’s twists and turns.

“Sienna was born via surrogate [and] I would like to thank my whole @ShondalandTV family for helping us enjoy these first few weeks privately,” she Tweeted.

Parenthood is a poignant yet bittersweet experience for Pompeo, who lost her own mother when the actress was just 4 years old.

“I try my absolute hardest every minute of the day to be the best mother I can to those children,” she adds. “Not having a mother [myself] growing up, being a mother is more significant than I can put into words.”

Sienna was born via surrogate & I would like to thank my whole @ShondalandTV family for helping us enjoy these first few weeks privately ❤️U

— Ellen Pompeo (@EllenPompeo) October 2, 2014

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— Michele Corriston with reporting by Elizabeth Leonard

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