Last November the 26-year-old suffered a miscarriage when she was six months pregnant.
Her first miscarriage took place in 2008 when she was four months pregnant with Chemical Brothers star Ed Simon’s baby.
The singer reportedly gave birth yesterday evening, with one of her friends announcing the happy news on Twitter.
Lily’s ex-boyfriend, DJ Seb Chew tweeted, “Sending love out to Lily, Sam and baby Cooper…YES!”
Allen has yet to confirm the news herself, but on Friday she took to her Twitter page to write, “Totes (totally) Amaze (amazing)”.
Reports say the newborn is a little girl, but additional details were unavailable.
It is Lily and Sam Cooper’s first child together. The couple married in the Cotswolds in June this year.