Ian James McDonald, 27, failed to return to Castle Huntly prison, near Dundee, yesterday after a period of approved leave.
Police Scotland said he had been following a public appeal.
He is known to frequent the Dundee area and was last seen in the city at about 3pm yesterday.
McDonald was described in the appeal as 5ft 7ins and slim with blonde hair, blue eyes and tattoos on both lower arms and on the centre of his neck.
He was last seen wearing a khaki jacket with a white zip, blue jeans and black trainers.
Police are appealing for anyone with information about his whereabouts to get in touch on 101.