The 23-year-old centre-back will move to the Ligue 1 club for the 2022-23 season, with Monaco then able to make the arrangement permanent for a reported €15million (£12.7m).
Monaco's purchase option could become mandatory if certain conditions are met, according to widespread reports.
Sarr joined Chelsea on a free transfer in August 2020 but was soon sent out on loan to Porto, where he made 19 appearances across all competitions.
🆕 AS Monaco are pleased to announce the arrival of Malang Sarr. The 23-year-old central defender joins on loan from Chelsea FC for one season with an option to buy.— AS Monaco EN (@AS_Monaco_EN) August 10, 2022
He returned to Stamford Bridge for the 2021-2022 season and became a member of the first-team squad, playing 21 times on all fronts, though only eight of those were in the Premier League.
In joining Monaco, Sarr returns to Ligue 1 after a two-year absence having previously been regarded as one of the most promising young defenders in Europe during his breakthrough as a teenager at Nice.
Sarr is Monaco's fourth signing of the window after Takumi Minamino, Breel Embolo and Thomas Didillon.
Monaco saw its UEFA Champions League qualification hopes ended on Wednesday (AEST) when a 3-2 defeat after extra time away to PSV saw them suffer a 4-3 aggregate loss in the penultimate stage of qualifying.