Birkhead, however, must return with 7-month-old Dannielynn for the full custody hearing in June, TMZ reported.
Smith's estranged mother, Virgie Arthur, objected to the ruling and could appeal, sources told TMZ.
Birkhead and other participants in the private custody hearing said they could not discuss the proceedings, but Birkhead said he was pleased.
"I guess all I can say really is that it was a good day for me in court," he said.
Arthur has been trying to reach a visitation agreement that would end her legal challenge for custody of the baby. After the Supreme Court hearing, she left in a taxi without speaking to reporters.
The judge scheduled another hearing for June 8.
Birkhead, a 34-year-old Los Angeles photographer, said efforts were "in the works" to obtain a passport for Dannielynn and change her birth certificate to remove the name of Howard K. Stern, Smith's last companion, and list him as the father.
Birkhead was revealed as the father by DNA tests this month. He said he hoped to leave the Bahamas for the United States with the baby "pretty soon."
Birkhead left the courthouse in a black Cadillac sport utility vehicle with Stern, who has been caring for the infant since her mother died in February, and supports Birkhead in the custody battle.
"I just want Dannielynn to have a good life," Stern said.
The girl could inherit a fortune if lawyers resolve challenges over her mother's estate in her favor. When she died of an accidental drug overdose in a Florida hotel room, lawyers were still wrangling over the estate of Smith's late husband, the Texas oil tycoon J. Howard Marshall II, estimated to be worth more than $1 billion.
Smith gave birth to Dannielynn in September only days before her 20-year-old son Daniel died of a drug overdose at her bedside.
Meanwhile, a judge who briefly heard arguments in cases involving Smith's death has filed a written plea of not guilty to misdemeanor marijuana possession, his attorney said.
Broward Circuit Judge Lawrence Korda, 49, was given a misdemeanor citation last month after police said they caught him smoking marijuana while sitting under a tree in a city park.
"All parties agreed to a May 7 (court date), at which point we hope to be in a position to resolve this," defense attorney Mike Dutko told the South Florida Sun-Sentinel.
Korda went on a temporary but indefinite leave of absence earlier this month. He continues to receive pay.
The fight over control of Smith's body began in Korda's courtroom and ended up being heard by Circuit Judge Larry Seidlin, who became known during the televised hearings for his relentless one-liners and tearful announcement of his decisions.
Korda later heard brief arguments in a related case, seeking to determine the biological father of Smith's daughter, Dannielynn. He ruled that a Bahamian court had jurisdiction over her custody.
The Associated Press contributed to this report.