With People confirming the happy news, no other information is known about the new addition to the family – Rose and Bobby are notoriously private about their personal life.
The 38-year-old Aussie actress and the American star already share 21-month-old son Rocco Robin together, and Bobby also has a 22-year-old son named Jake from a previous marriage to actress and screenwriter Jenny Lumet, 50.
Rose first announced her second pregnancy in Jones earlier this year.