"I'm so happy for Tacko. He handled this with such humility, and we're so thankful the NCAA understands his story," Jones told ESPN.
The Knights opened the season at Davidson on Saturday night. Fall got the start.
"I would also like to thank the NCAA for allowing me to continue to pursue my dream here at UCF as a student-athlete," Fall said Friday in a statement.
Fall's guardian for the past two years, Amanda Wettstein, told ESPN on Tuesday that they were prepared to sue the NCAA if the waiver wasn't granted.
"I cannot stop crying. It was always about more than basketball. We are so grateful to everyone," Wettstein tweeted shortly after hearing the news.
The NCAA had informed Central Florida last week that Fall wasn't allowed to practice with the team after it was determined that the NCAA was only accepting seven and a half of his core courses from Liberty Christian Preparatory School in Tavares, Florida.
Wettstein told ESPN that Liberty Christian, which has been in existence for 25 years, has been placed under an extended evaluation status by the NCAA for a minimum of two full academic certification cycles.
Fall grew up in Dakar, Senegal, and spent his freshman and sophomore years in his native country before arriving in the United States. He is an engineering major at UCF.
The Associated Press contributed to this report.