Casey has joined the Cottagers after trialling for the past two weeks.
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He will see out the season with Fulham's U21 team.
Speaking to fulhamfc.com, the 18 year-old midfielder said: "This is my first professional contract, so it feels great. I'm really excited to get going.
"I want to finish the season strongly, go as far as we can in the PL2 Play-Offs, and then make my way into the First Team as soon as possible."
Casey enjoyed a decade with the Gunners, finishing with a strong season as a second year scholar, scoring 18 goals in 21 appearances in the U18 Premier League, including two against Fulham.