A 17-year-old ball playing centre-back, Murphy was most recently with Hartlepool United, and he will now link up with Colin Omogbehin's Under-18 side.
Speaking to fulhamfc.com, Murphy said: “Over the past couple of weeks lots of clubs have been in contact with us but once Fulham made it clear that they wanted to sign me it was an easy decision to come here.
“The facilities are brilliant, the coaching staff are top class, and there is a pathway for young players to progress into the First Team.
“You only need to look at Ryan Sessegnon and what he's achieved at such a young age. He is somebody that I look up to massively.
“I want to work hard here and show everybody what I can do. I can't wait to get started."