The 33-year-old striker moved to the Ligue 1 outfit on loan for the rest of the season on Friday.
"I'm happy, excited and a little bit nervous to be honest," he told Monaco's official website. "I look forward to start training with my new teammates and open a new chapter in my career."
Monaco vice president Vadim Vasilyev added: "Dimitar will bring us all his experience and talent. His coming is of course connected to the Radamel Falcao's injury. He played in big clubs as Manchester United and he's a big striker.
Monaco are currently second in Ligue 1 with 48 points from 22 matches.