The 18-year-old, who has made two first-team appearances for the club this season, is regarded as one of the best young prospects in England.
"I think it's a good achievement to get another contract at the club. I enjoy playing here and I hope it continues. I was seven when I joined the club and I've come a long way. It's been a good journey and I've had some ups and downs but I think I'm doing pretty well for myself at the moment," he told the club's official website.
"It was definitely a good experience for me to come on and make my debut. It was a surprise to me and I'm glad that I did it. I want to get my Premier League debut under my belt because that would be another good experience for me. I just have to keep working hard and hopefully the manager notices me."
Fanimo has been a key member of the club's development squad this season.