Johnson was born in Orlando and moved to Ohio at the age of 14.
He played four seasons at Dayton, where he averaged 12.4 points and 6.4 rebounds per game as a senior.
Magic officials liked Johnson during the draft scouting process, but his chances of making the Magic roster are extremely slim.
Orlando now has 20 players on its roster. The team must get down to 15 players before the start of the regular season.
Johnson's signing might be a tacit admission that Afflalo will be out of action a while longer. Afflalo has a left-hamstring strain, and team officials want the muscle to heal fully before Afflalo practices or plays.