The 60-year-old, who had also been linked with the vacant managerial positions at West Brom and Fiorentina, has signed a two-year contract with the Ligue 2 side, with the option for a third.
A statement on the club's official website said: "AS Monaco are delighted to announce the appointment of Claudio Ranieri as coach.
"This appointment follows a search and a rigorous selection process during which Claudio Ranieri has clearly established itself as the best candidate for the position.
"He is now considered one of the best coaches in European football and brings to AS Monaco all the richness of his experience and achievements in football."
Ranieri replaces Marco Simone, who was dismissed at the end of the season, despite guiding les Rouge et Blanc to a credible eighth-placed finish in the French second-tier with the team bottom of the table upon his arrival last September.
It also marks a return to coaching for the Italian, who had previously endured a disastrous spell in charge of Inter last term, and was sacked in March after a dismal run of results had left the club languishing in mid-table.
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