Bakayoko reportedly also had offers to weigh up from other European sides, including Premier League rivals Manchester United, but he is confident that he has made the right decision by joining the reigning champions.
"For me this is the biggest English club, and I hope to achieve great things here. I am very proud," he told the club's official website. "Chelsea is a great club with a great history, and they are the champions of England.
"My wish was to be at the best English club there is today. I am very happy and proud for me, my family and the people who have been following me for a very long time.
"Now the work starts for all of us together to progress. I know that the Premier League is a very difficult championship, one of the most difficult in the world. It is very physical and I know you must be in fighting form to compete in this league.
"I have got a great reception and I'm very much impressed by the facilities here. Everything is much bigger than I have known, and it seems like the perfect place to play football. I haven't been to Stamford Bridge yet but I can't wait to see this big stadium."
Bakayoko has been handed the number 14 shirt for the 2017-18 season after putting pen to paper on a five-year contract.