There have been numerous attempts to explain the emergence of this expression, which seems to have swept into popular use in the US during the mid-19th century. Most of them are pure speculation. It does not seem at all likely, from the linguistic and historical evidence, that it comes from the Scots expression och aye, the Greek ola kala ('it is good'), the Choctaw Indian oke or okeh ('it is so'), the French aux Cayes ('from Cayes', a port in Haiti with a reputation for good rum) or au quai ('to the quay', as supposedly used by French-speaking dockers), or the initials of a railway freight agent called Obediah Kelly who is said to have written them on documents he had checked.
