Bakayoko helped Monaco win the French league title in 2017 before joining the Blues but the principality club narrowly avoided relegation last season and are second from last after taking only two points from their first four games of the campaign.
Having re-joined them from Chelsea on loan for the season, the French midfielder hopes to help turn things around for the Monegasques.
"I am very happy to come back to AS Monaco, a club with which I keep fantastic memories," said the 25-year-old.
"Since 2017, I had the opportunity to have two very good experiences with Chelsea and Milan.
"I hope to be able to integrate as quickly as possible in this collective, in an environment that I already know, and especially with the desire to bring to the group what I know how to make a good season."
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