The 29-year-old has been with the team since they returned to the sport in 2010 and is hopeful that they can maintain their recent dominance in the coming years.
"So this is it - we're actually standing here now as world champions," he told the Mercedes workforce.
"This has been a long time coming. Since I joined at the start of this project I expected this day to come as I've had such strong belief in this group of people from right back on day one. To be a part of that and to have finally achieved this championship in such dominant fashion is a great feeling.
"I'd like to say a big thank you to everyone for all their hard work. I hope they can really enjoy this moment, that there will be many more great moments to come and that this is just the beginning of a long era of success for the Silver Arrows."
Mercedes have also dominated the drivers' championship this year, with 17 points separating first-placed Hamilton and second-placed Rosberg.