Leonardo Jardim's charges needed just one point to seal the French championship at the Stade Louis II, and goals from Kylian Mbappe and Valere Germain ensured that the Monegasques got over the line comfortably.
Monaco's title win is their first in 17 years and puts a stop to Paris Saint-Germain's run of consecutive championship triumphs, which has not been allowed to go beyond four.
Monaco continued to pressure as Mbappe, Falcao and Thomas Lemar all weighed in with chances, but were unable to seal the clinching goal until right at the death.
Germain tapped home Lemar's pass with the last kick of the game to ensure that Monaco recorded their 29th league win of the season and secure a famous title triumph for the club.
Monaco move six points clear of deposed champions PSG and will finish the season with 95 points if they win their last game of the campaign at Rennes on Saturday.