Jones, a freshman early enrollee at Florida, entered the transfer portal last month after participating in spring practice.
Two Florida students accused Jones of sexual battery, stemming from an alleged April 6 incident at an on-campus residential housing complex. Jones was not charged as the students ultimately did not pursue legal action against him.
The university released two reports stating the female students visited Jones and freshman cornerbacks Jaydon Hill and Chris Steele at their dormitory. The two female students alleged Jones forced himself on them.
Jackson State would only confirm Jones' arrival, declining to comment on the allegations.
Steele complained to Florida officials about Jones and requested to change dorm rooms, but he was not moved and ultimately left the program, transferring to Oregon last week.
Jones, ESPN's No. 11 dual-threat quarterback in the 2019 class, played in the Gators' spring game April 13. Florida coach Dan Mullen said last week that the team immediately suspended Jones after receiving reports of the alleged sexual battery.