The child's mother, 39, who was Playboy magazine's Playmate of the Year in 1993, died of an accidental drugs overdose in February.
Emerging from a Bahamas court, where the DNA hearing was held, Mr Birkhead, 34, walked up to a bank of microphones and said: "I hate to be the one that said I told you so - but, I told you so."
The tests showed that Mr Birkhead is 99.99999 per cent certain to be the father.
Howard K Stern, the lawyer and boyfriend of Anna, had claimed to be the baby's father when he signed her birth certificate.