The Briton's victory, coupled with a second-placed finish for Nico Rosberg, secured the constructors' championship for the Brackley-based outfit.
"I'm so happy to be here. We have had another amazing week, Russia and the people have been fantastic and I am looking forward to being here for many more years to come," Hamilton said.
"Nico did a great job to recover today and as a team we did a great job to win the first constructors' championship for Mercedes. It's a wonderful day."
The win, which was Hamilton's ninth of the season, has extended his lead over teammate Rosberg to 17 points at the top of the drivers' standings.