Jackson has penned a new two-year contract extension to 2033.
"I am feeling very good and am very happy to sign a new contract and stay at the club," the 23-year-old said.
"It feels great the club has confidence in me. I am working very hard. I am very happy to extend my contract and stay here for many years."
The Senegalese also stated: "The first season for any player or any striker that comes to Chelsea is not easy, but I did okay.
"I am not very happy with 17 goals because I played the whole season without injuries, but it’s okay. I did good, now I hope to continue and do amazing. I am still in the learning process, learning every day, and trying to improve what I can do, and work on what I cannot do.
"It was not hard to adapt to the club because I could speak English and I’m a social person. It was easy to talk to everybody and get to know people. The only problem was the weather, but I got used to it!
"On the pitch I’m friends with everybody. It will always be like that. I hope this year together we will do more than last year and win something."