UK, 1938—old-fashioned informal British-English adjective meaning ‘in good order’, ‘fine’—origin obscure: perhaps from Hindi ‘ṭhīk hai’ (‘all right’) or from ‘the ticket’ (‘the correct thing’); or it may simply be a purely fanciful formation
USA, 1956—jocular variant of equally jocular ‘see you later, alligator’ (1952)—recoined on separate occasions by various persons, independently from one another