The 26-year-old, who made 22 appearances for the reigning Ligue 1 champions this season, joins Saints on a three-and-a-half-year deal for a reported fee of £19m.
Carrillo will reunite with Southampton boss and compatriot Mauricio Pellegrino after previously working with him at Argentine giants Estudiantes.
"I'm very happy," Carrillo told the official Saints website. "It's a great feeling to be a part of this club.
"Lots of things attracted me. I know Southampton from watching the Premier League from when I was small, I've always regarded it as the most important league in the world.
"I obviously know the coaching staff, I've worked with them in Argentina and I also spoke with some players who were former teammates in Argentina, who are now playing in the Premier League and they told me all about the club and gave it a shining reference. Therefore, I had no doubts when I took the decision."
Carrillo has scored 20 goals in over 50 games for Monaco since signing from Estudiantes in 2015.