The Spurs striker was reportedly at his fiancée's side as she gave birth to a baby girl weighing 7lbs, 9oz.
A friend of the couple told the Daily Mail: "Abbey and Peter are over the moon. They haven't picked a name yet, but they are completely in love with her."
A spokesman confirmed that mother and baby are both doing well.
Crouch and Clancy are thought to be planning a summer wedding.
> Ten Things About... Abbey Clancy