The France international joined the Blues from Monaco for £40m in the August transfer period but has had to make due with limited game time due to the form of N’Golo Kante.
However, with Kante facing several weeks out with injury, Bakayoko is set to get his chance to shine and the 23-year-old hopes he can do just that.
“It’s going really well,” he told Evening Standard.
“I feel like I have found a family here. My team-mates have welcomed me and treated me from the start as if I was here for a long time and a part of their family.
“From the moment I started, I’ve felt like I get on well with the coach and I know what he wants.
“I am someone who can fulfil a lot of different roles on the pitch. I’m not saying I’ve got no improvements to make and in the future I will always work to get better.
“People who play up front are there to score goals, but I’m there to bring everything together in the middle of the pitch.”