The 16 year-old has earned scholarship forms after impressing in preseason trials.
Kondau-Wall joins Fulham from local academy Impact FC, he also had a previous spell with Charlton Athletic.
The teen will begin his time with Fulham with their U18 team and told fulhamfc.com: “It feels amazing. It’s a dream come true signing at this amazing football club.
“My football journey began at the age of eight, playing grassroots. I was picked up by Charlton Athletic at the age of 11 but got released. It was a big setback, but I knew I’d come through it and come back stronger, and now I’m here signing for Fulham Football Club.
“In one word, I’m powerful. I work hard and I want to win. My footballing idol is actually a former Fulham player. Mousa Dembélé, what he did in his career, I want to bring all of that into my game.
“I want to make my Under-21s debut and hopefully sign a professional contract at this amazing club. To sign for a Premier League club, it’s amazing.”