Abbey gave birth to the couples first child on 15 March.
The pair have named their baby girl, who weighed in at seven pounds nine ounces, Sophia Ruby.
A source confirmed the news, saying:
"Mother and daughter are doing brilliantly.
"Abbey and Peter are over the moon. They are completely in love with her."
Twenty-five-year-old Abbey has said previously that she thought she was having a boy.
She told This Morning hosts Eamonn Holmes and Ruth Langsford:
"I think it's a boy from looking at the scans...it's too boisterous to be a girl!"
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