William Webb Ellis, a pupil at Rugby.
Hence the name of the game.
Actually, carrying the ball was a commonplace in many of the regional variants of the sport played throughout England prior to the attempts of the public schools (private schools in U.S. parlance) to establish one set of national rules, which in reality failed and gave rise to the officially defined, separate sports of rugby football and association football.
Ellis gets credit only for doing at a public school in what was supposed to be an association game that which was done commonly elsewhere in England.