Vettel needed to finish in at least fifth place to win the title, but he instead came first in Greater Noida to cement his place at the top of the standings.
Mercedes' Rosberg secured himself a spot behind his fellow German on the podium, while Lotus' Romain Grosjean completed the top three.
"Sebastian has done an amazing job and deserves to be champ," Rosberg is quoted as saying by BBC Sport. "We will do everything possible over the winter to be competitive next season."
The Formula 1 calendar continues at the start of next month with the Abu Dhabi Grand Prix.