Old English unbindan, "to free from binding," from un- (2) "opposite of, reverse" + bind (v.). Similar formation in Old Frisian unbinda, German entbinden, Dutch ontbinden. Literal and figurative senses both present in Old English.
Su hut u unbindes ofer eoru bi unbunden in heofnum. [Lindisfarne Gospels, Matt. xvi:19]
Unbound is from Old English unbunden, in literal sense. Figurative sense first attested late 14c.; of books from 1540s.