The 37-year-old actress and her husband Will Kopelman welcomed their first child, Olive, last Wednesday and have asked for privacy during this "special time".
The happy couple issued a statement reading: "We are proud to announce the birth of our daughter, Olive Barrymore Kopelman, born Sept. 26th, healthy, happy and welcomed by the whole family.
"Thank you for respecting our privacy during this most special time in our lives."
The Going the Distance star – who began dating art consultant Will in 2010 – tied the knot in June in an intimate Jewish ceremony on her estate in Montecito, California.
The couple were keen to get married before the baby was due in the autumn and enjoyed a relaxing honeymoon in Big Sur after the big event, which Drew described as a "perfect" day.
The actress - who has been married twice before - has often expressed her desire to start a family with Will.
She recently said: "I can’t wait until I have my children. I just want to build fun, great things for my family."
Drew has also voiced her wish to have a baby daughter in the past, musing: "I do feel I'm going to have a child at some point. Maybe a little girl. I feel it, but I don't know if it's going to happen. We'll just have to wait and see."