Earlier this month, a Bahaman court revealed test results confirming Birkhead is the father of the late model's 7-month-old child, Dannielynn. Smith's longtime companion, Howard K. Stern, was listed on the child's birth certificate as the father.
The child's birth certificate is being changed as a result of Wednesday's hearing and she is expected to get her first passport, the syndicated show reported.
Birkhead reportedly had to agree to return to Nassau in June for what should be the formal resolution of the girl's custody.
Smith died Feb. 8 in Hollywood, Fla., of an accidental drug overdose.