Leanca Rostas, 34, and Marcel Rostas, 35, and their one-year-old Matie had last been seen at the University Hospital of Wales in Cardiff at about midnight on Wednesday February 16.
Police investigations established that the family travelled to Scotland and they were thought to have gone to the Fife area.
On Friday morning, Police Scotland said that the family, from South Wales, has been traced safe and well north of the border.
