"What a crazy and amazing last couple days," she wrote.
"I am so excited to introduce you to our baby girl: Presley Belle Hudson! She ended up being 7lbs 7oz. and 20.75 inches long, and we are already so in love. She also has a full head of brown hair, and the sweetest personality!
"Thank you so much for all your prayers and well wishes.. feeling incredibly emotional and blessed!" she added.
Cooper made an Instagram account for Presley and posted a photo of her baby girl from the hospital.
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"My mom is already way too excited about putting bows in this wild hair," Cooper captioned the post. "But I'd rather just take a nap, and make new friends like you ;)."
Cooper announced her pregnancy in January alongside a message to her then-unborn child.
"Dear Baby, I hope you know that I already love you more than I could have imagined possible. I hope you chase all of your dreams, and I'll be supporting you the whole way," the star wrote.
"I hope you get my spirit and sense of humor, and never stop laughing. I hope you get your dad's thoughtfulness and work ethic, and never stop being curious," she said.
"I hope you can ignore the negativity of the world, and always stand up for yourself."
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