A Bahamian court cleared the way Friday for Anna Nicole Smith’s ex-boyfriend to leave with their baby daughter, rejecting an appeal by the mother of the former reality TV star.

The judges ruled that a U.S. court would likely have the final say in the custody dispute between Virgie Arthur and Larry Birkhead, who was confirmed as the 7-month-old baby’s father after undergoing DNA testing.

Arthur was challenging a judge’s decision this week to let Birkhead leave the island chain with Dannielynn. ...