Monaco was relegated from the French top division for the first time in 35 years after losing 2-0 at home to Lyon on the final day of the Ligue 1 season on Sunday.
Third-bottom going into the game at Stade Louis II, Monaco needed a positive result to stand any chance of avoiding the drop but fell to second-half goals by Pape Diakhate and Lisandro Lopez.
French champion in 2000 and Champions League finalist in 2004, Monaco - which sacked coach Guy Lacombe in January and replaced him with Laurent Banide - will play in the second tier next season for the first time since 1977.
"This is a big loss for French football," said Banide. "We just weren't good enough to stay in Lige 1 - you have to respect the laws of football."