The west Londoners agreed a deal to sign the 18-year-old in October, with the move now officially completed on New Year's Day after the transfer window re-opened.
Traore joined Jose Mourinho's side as a trialist and was a regular fixture in the Blues' preseason tour of Asia, scoring against a Malaysia XI and Indonesia All Stars.
The teenager is delighted to have signed for the Stamford Bridge outfit, and, having already sung the customary initiation song, is now looking to emulate African superstars such as Didier Drogba.
"I was very happy. It was a good experience with all the senior players and I learned a lot from them," Traore said of his preseason trail with Chelsea. "I was very proud, so it was a dream for me to be there every day and playing games. Of course I was a little bit nervous but after two or three days I was okay. On the pitch I was comfortable, I wasn't nervous once I was on the pitch.
"Jose Mourinho spoke a lot during training and he is one of the best managers, maybe the best in the world. He is a very good person and it is a dream for me to work with him. I can now say I am living a dream. At Chelsea I look to follow the way of some African legends like Didier Drogba, Michael Essien and now Samuel Eto'o."