The midfielder completed his transfer to Stamford Bridge from Monaco on Saturday, signing a five-year deal.
The Premier League champions have reportedly paid £40 million for Bakayoko and he is expected to line up alongside Kante for Chelsea, with Nemanja Matic, a regular in Antonio Conte's first season, linked with a move to Manchester United.
Having left Monaco, the 22-year-old is keen to build a partnership with Kante that could provide success for both club and country.
"N'Golo Kante has proved it all," Bakayoko told Chelsea's website.
"He was the best player in the Premier League last season in the middle of the pitch and that is not easy.
"To play alongside him would be something very good for me and it can help me progress.
"I have played a match with him for the French national team so we know each other very well and I hope we can do beautiful things together this year."
"I have the ambition to play as many matches as possible, to progress as much as I can with a great coach like Antonio Conte, and then I have the objective of taking part in the World Cup at the end of the season," he said.
Bakayoko has also praised the influence of former Chelsea star Claude Makelele, who worked with him at Monaco, on his career and revealed another Blues icon, Didier Drogba, is an inspiration.
"Yes, Makelele helped me greatly," he said. "When he arrived at Monaco I wasn't a very, very good player, but I had a lot of discussions with him, he gave me a lot of advice, and he allowed me to play my style of football more simply.
"Drogba has had a stellar career and he managed to do so many great things, first at Marseille and then here at Chelsea.
"He is definitely an example I wish to follow, be it the footballer or the person himself. He showed the whole world what he was and I saw that and admired it."