The 19-year-old made 24 league appearances last year, scoring one goal as Rennes finished 12th in the French top flight.
Big-spending Monaco challenged similarly wealthy Paris Saint-Germain for the Ligue 1 crown in 2013-14, but ultimately fell short as PSG took the title by nine points.
On Friday, Bakayoko appeared set for a switch to Monaco as he told Rennes' official website: "Monaco is gaining momentum in France and worldwide.
"This is a good thing. This is a new challenge.
"It is true that I leave after a steep rise after only one professional season at Stade Rennais. I was right here but it happened naturally.
"It saddens me still to leave the club because I spent six wonderful years here. I was trained in Rennes.
"I hope Stade Rennais have a great season. I wish the players and supporters the best."
A Rennes stataement confirmed that Bakayoko will move to Stade Louis II upon passing a medical with Leonardo Jardim's side.
