The 21-year-old winger has signed a five-year contract, while reports suggest the move has cost Atletico in the region of €20 million (£14.3m).
Carrasco, who has been capped three times by Belgium, is viewed as a replacement for Arda Turan after the Turkey international joined Barcelona earlier in July.
"We are very satisfied with the agreement reached with Monaco, because Yannick is a player with huge prospects and with an incredible future," said Atletico’s sporting director Jose Luis Perez Caminero.
"He is a player with great speed, who's excellent at driving the ball and has a great shot. He will contribute perfectly to our aim of increasing the quality of our team and the competitiveness in the group.
"I am convinced that he will contribute a lot to the team."
Carrasco is Atletico’s third signing of the summer after the arrivals of Luciano Vietto and Jackson Martinez.