The 19-year-old is said to have impressed during a trial with the club in March, and the teenager's agent has since declared that an agreement has been reached for Lewis to join the Gunners.
Speaking to Norwegian outlet VG, Fram Larvik sporting director Jostein Jensen said: "Yes, we can confirm that. I have been told that he has signed for Arsenal. We wish George good luck."
Lewis, who mainly operates on the left-wing but can also play as a second striker, arrived at Norwegian third-tier side Fram last summer from Tromsdalen.
The teenager will supposedly join Steve Bould's Under-23 side at Arsenal rather than jumping straight into the first team.