The 25-year-old model and her soccer star fiance Peter Crouch became parents for the first time on 14.03.11 and are thrilled with their new arrival.
A source said: "Mother and daughter are doing brilliantly.
"Abbey and Peter are over the moon. They haven`t picked a name yet, but they are completely in love with her."
The baby weighed in at 7lbs 9oz.
Peter, 30, is said to be looking forward to celebrating his daughter`s birth with his Tottenham Hotspur teammates.
One pal said: "The Spurs boys have been texting him congratulations - and promising to help him wet the baby`s head."
Abbey - who has been in a relationship with Peter for five years and got engaged almost two years ago - is likely to be surprised by the gender of the infant as she previously admitted she thought she was carrying a boy.
She said soon after confirming her pregnancy: "I think it`s a boy from looking at the scans... it`s too boisterous to be a girl."
The couple are thought to be planning to marry this summer.