Gregory was an ESPNChicago.com all-area selection as a junior last season, when he completed 84-of-120 passes for 1,600 yards and 28 touchdowns and rushed for 919 yards and 16 touchdowns.
In Friday's season opener, he threw for two touchdowns in a loss to Mount Carmel.
"He's a really smart kid as far as playing the quarterback position," Simeon coach Dante Culbreath said. "I don't think you can find a smarter kid. He's going to pick up whatever he has to pick up. He's gotten a little bigger, a little stronger this season."
Arkansas now has 18 Class of 2012 commitments.
Scott Powers covers high school and college sports for ESPNChicago.com and can be reached at firstname.lastname@example.org.