Baby Marnie Rose was born Tuesday.
Allen, 27, and husband Sam Cooper married in June 2011 and are the parents of a 13-month-old daughter named Ethel Mary.
People.com said the recording artist's representative declined to confirm her pregnancy in July, but Allen tweeted on New Year's Eve she was "only planning on spending a few days of  pregnant. Unlike the last 3 years."
Allen previously suffered a miscarriage and had a stillborn child before giving birth to little Ethel.