The pacey 18-year-old, who looked set for a career in sprinting, can play in a variety of attacking positions.
Jeffrey is highly regarded at Arsenal after scoring six goals in 19 appearances for the youth team last season.
He is available for Saturday's visit of Colchester.
Meanwhile, goalkeeper Steve Arnold has signed a two-year contract extension after a fine start to his Stevenage career.
Arnold told the club's official website: "I was definitely happy to sign the deal. I came here in the summer as a second choice and managed to get my way into the team which I was delighted with."