"I couldn't eat or sleep for two weeks, I was just so nervous!" she tells PEOPLE in this week's exclusive cover story.
Starting a family with art consultant Will Kopelman, whom Barrymore married last June, has meant everything to the actress.
"I really wanted a wonderful traditional home for my kid," she says. "Will comes from a strong family, he provides a strong family ... It just makes me so emotional because it's like a miracle."
Despite the overwhelming emotion of love, Barrymore, 37, says no one prepared her for the responsibility she'd feel after her daughter was born.
"You have the highest highs and yet you're facing the biggest fear of, 'How do I keep someone alive?' "
One of Barrymore and Kopelman's favorite things? Singing "Good Morning" from Singin' in the Rain to get little Olive to smile. Says the actress: "It's like the biggest crush I've ever had in my life!"
For exclusive photos of the whole family, plus more from Barrymore's emotional interview, pick up this week's issue of PEOPLE, on newsstands Friday
Drew Barrymore Introduces Daughter Olive
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Drew Barrymore Introduces Daughter Olive
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Drew Barrymore Introduces Daughter Olive
