The table-topping Blues won all six of their Premier League games last month, including a 3-1 triumph at title rivals Manchester City, conceding just three goals while scoring 13.
"I'm very proud," Conte told the Chelsea website. "It's a great honour for me but I want to say thanks to all of my players, my staff and the club because we won the award together. Now it's important to continue to work very well together.
"I enjoyed my first Christmas period a lot. This type of atmosphere only happens in England and it was fantastic. I hope to experience it again many times in the future. When you win you usually see a lot of positive things and every game was different. We won six matches and to do that, especially in December, is very difficult.
"If I had to pick out one game I would choose West Brom, because it was very tough and we scored with 15 minutes remaining. My players showed me great character and a strong will to win right until the end that day, which I always like to see."
Conte's side next travel to reigning champions Leicester City when league action resumes tomorrow.