The 18-year-old made seven Premier League appearances and featured 10 times for the first team, showing plenty of promise.
He also impressed for Fulham's Under-21s, scoring four goals in just five Premier League 2 matches at an average of one goal every 92 minutes.
“I’m very happy to be a permanent Fulham player. From my first week here, it was very good – I felt like I was a part of the Fulham family,” Kusi-Asare told FFCtv.
“The changing room was very nice, team, staff, so I’m very happy to stay here.”
Vice Chairman and Director of Football Operations Tony Khan added, "I’m thrilled to welcome Jonah Kusi-Asare to Fulham on a long-term contract.
"We believe that he is a very talented young player with massive potential and a bright future, and we’re very happy that Jonah is joining the Club permanently now following his time with us on loan."