The baby, named Harper Seven, was delivered on Sunday at Cedars Sinai hospital in Los Angeles.
In a statement on his Facebook page, England footballer David said: "I am so proud and excited to announce the birth of our daughter Harper Seven Beckham.
"She weighed a healthy 7lbs 10oz and arrived at 7.55 this morning, here in LA. Victoria is doing really well and her brothers are delighted to have a baby sister xx."
The Beckhams, who married in 1999, already have three boys - Brooklyn, 11, Romeo, eight, and Cruz, five.
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"Happy and healthy she arrived at 7.55am this morning at Cedars Sinai hospital in Los Angeles and weighed 7lbs 10oz."
In another posting, he added: "Brooklyn, Romeo and Cruz are excited to welcome their new baby sister to the family."
Friends of the couple were quick to send their congratulations.
A delighted Mel B, who is expecting her third child later this year, expressed her excitement on Twitter, writing:
"congrats!!! Yipeee another spice baby is born, damn it wish it was me this AM cos I feel like I'm about to POP!"
Former Spice Girl Emma Bunton also tweeted: "Big kiss to @victoriabeckham can't wait to meet your gorgeous little girl!"