The 21-year-old is the latest youngster to join Atletico who have also brought in Argentine forward Luciano Vietto from Villarreal since the end of last season.
Carrasco, who joined Ligue 1 Monaco from Racing Genk in 2010, has agreed a five-year contract, Atletico said on their website.
They did not disclose financial details but Spanish media reported that the club had paid 15 million euros (11 million pounds) for 75 percent of the player's rights, with Monaco holding on to the remaining 25 percent.
"Yannick is a player with massive prospects who has an incredible future," Atletico sporting director Jose Luis Perez Caminero said. "He is a player with great speed, excellent ball skills and a great shot.
"He will contribute perfectly to our goal of lifting the level of the squad and the group's competitiveness. I am convinced he will give us a huge amount."
Atletico have also agreed to sign Colombia striker Jackson Martinez from Porto, the Portuguese side said this month, although the Spanish club have yet to confirm the deal.
The Madrid team have sold two key players in the close season with Turkey captain Arda Turan joining Spanish and European champions Barcelona and Croatia international Mario Mandzukic moving to Italian champions Juventus.
La Liga is due to begin the weekend of Aug. 22-23.
Atletico have qualified for the group stages of next season's Champions League.
($1 = 0.8983 euros)
(Reporting by Iain Rogers, editing by Tony Jimenez)
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