The practice of using smoke to 'calm' bees is certainly centuries old, and was probably discovered independently at various times and locations in the history of bee keeping and wild honey collection.

Although highly effective, it's currently not known exactly how it works. One theory is that it disrupts the bees' ability to sense chemical distress pheromones released by other, disturbed, bees in the colony. (ref. Journal of Insect Behavior volume 8, pages 11–18)

Others speculate that there might be chemicals in the smoke which have some kind of soporific or narcotic action on the insects (e.g. carbon monoxide) Or that the smoke reduces available oxygen levels, causing the bees to be less energetic.

Another (informal) suggestion is that it's an inbuilt reaction to forest fires - when detecting smoke, the bees gorge themselves on honey before abandoning the hive, and the soporific effect comes from the excess honey they've consumed.

Further technical info. : Ph.D. thesis (David Newton). University of Illinois at Urbana-Champaign