Well, the easy answer is there is no easy answer! As with so much in the world of etymology, no-one is absolutely sure. According to Oxford Dictionaries, there are loads of places it could have come from – although all equally unproved and unlikely. Could it have come from the Scottish och aye (yes!) or the Greek ola kala (it is good). Or maybe it’s French – it has been suggested it comes from aux Cayes (Cayes being a port in Haiti with a reputation for good rum) or au quai (to the quay, as said by French-speaking dockers). It certainly became popular in the mid 19th century USA so maybe the theory that it comes from the Choctaw Indian oke or okeh (it is so) could hold some water? Or maybe the initials of a railway freight agent called Obediah Kelly? More plausible, but equally without hard historic evidence, is that it perhaps came over with the slaves, being similar to a word meaning all right, yes indeed in various West African languages.
But, probably, none of the above. The most popular explanation is that comes from orl korrekt , a jokey misspelling of all correct used in the US in the 1830s. It became more popular when used in the 1840 presidential campaign for the Democrat Martin Van Buren – nicknamed ‘Old Kinderhook’ (after his birthplace in New York State). His supporters formed the OK Club which served to popularise the term (but not get poor old Martin re-elected).
Nowadays of course it is used across the world and in many different guises – from the “formal” okay to the quick and easy OK. If you have teenagers, you’ve also probably received a text just reading K on occasion – I know I have! We have A-OK if we want to go all space age, okey dokey and okey doke (remnants from the 30s) and even okely-dokely from The Simpson’s Ned Flanders. But who, you may (or may not) be asking, is Mikey? Anyone know?!