He scored against Greece, Ivory Coast and Japan as they topped Group C before netting twice, one a sublime volley, during the 2-0 last-16 win against Uruguay.
His final goal was a late consolation from the penalty spot as Colombia lost 2-1 to Brazil.
Rodriguez's goals helped Colombia progress further than they had before at a World Cup.
Germany's Thomas Muller finished second in the Golden Boot race with five goals, the same total he had when he won the award in 2010.
