The 50-year-old Roman, who was shown the door at San Siro by Massimo Moratti in March, is set to be unveiled as Marco Simone's successor in the coming days
The Roman has put pen to paper on a two-year contract with the Ligue 2 outfit, with the option for a third, according to Sky Sport24.
Ranieri had been heavily linked with former club Fiorentina in recent weeks, but the Viola now look set to appoint Vincenzo Montella as their new coach.
The vacancy at Monaco sprang up recently following the dismissal of former Italy international Marco Simone, who had led the Rouge and Blanc to a disappointing eighth-placed finish in the French second division.
The side from the Principality are funded by Russian tycoon Dmitry Rybolovlev and recently announced the signing of Andrea Raggi for next season.