The 37-year-old designer insisted that their family was now "complete," a friend revealed -- and her soccer star husband, 36, agreed.
LA Galaxy star Beckham is said to understand why his wife is calling a halt to more children after her difficult pregnancy gave her back pain and bunions.
The friend said, "Victoria is determined not to have to go through that again."
The seven-pound, 10-ounce, sister to Brooklyn, 12, Romeo, eight, and Cruz, six, was born in Los Angeles on Sunday.
The Beckhams' daughter is believed to be named after a Disney character her three brothers adore -- called Harper Finkle.
The boys are hooked on the US TV show "Wizards Of Waverly Place," in which the name is that of a magical family's pal, played by actress Jennifer Stone, 18.
A friend revealed, "The boys love 'Wizards Of Waverly Place' and have been very vocal in helping to name their new sister. David and Victoria think it is a lovely name. The whole family is pleased with the choice -- the boys are very happy."
The new mum drew the line at Finkle being the middle name of the daughter she has longed for. Instead the couple agonized for nine hours after the birth before eventually plumping for Seven -- soccer idol Beckham's number when he played for Manchester United and the English national soccer team.
The friend explained, "Seven is something they had talked about. They were still not certain when the baby was born but it all seemed to fall into place. She was born in the seventh month in the hour of seven and weighed seven pounds. It just seemed right. David is keen on the meanings and power of numbers. We all hope it will bring her luck."
David Beckham wept as Harper was delivered by C-section at the Cedars Sinai hospital. He has since given his wife a diamond necklace he designed himself -- and has had a matching one made for his daughter.
A source added, "With three great boys and now a beautiful girl Victoria is insisting their family is complete."