Swing music started to become identifiable in the 1930s. It evolved out of earlier forms of jazz, so no one really "invented it", and even the earlier "swing" bands wouldn't have known they were going to be classified as a different kind of jazz. The biggest difference was heard in the rhythm section, where the beat "loosened up" a whole bunch, and the cymbals and bass player started to play a more active role.

Sorry for the brevity, I'm on the road at the moment.