Wade has penned a new deal to 2027.
The 17 year-old told the club's website: "I feel proud to extend my stay as it means a lot to me. It’s every boy's dream to sign for a club like Chelsea, and to continue my journey is a surreal moment. I almost can’t quite believe it!
"But with all the endless hours and sacrifices I have had to make to get here, it shows my love for the sport, and playing football every day is something I love doing.
"I want to continue to develop and improve, which hopefully will see me progress into the Under-21s squad before following the pathway to the men’s team.
"Being at Chelsea, being surrounded by other Academy players who have stepped into the senior side, gives you even more ambition and drive.
"The pathway is so clear and having the men’s building always in eyeline – across the road – just shows how close the opportunities are and the possibilities of what could happen."
"I’m looking forward to continuing my hard work and doing what I love doing - playing football.