The teenager was released by the Gunners this week.
"Jeffrey loved his time here on trial last season, and I can't actually believe how we got him as easily as we did," Deepdale chief Graham Westley told the Lancashire Evening Post.
"He has very exciting talents, not least his pace. It won't be a surprise if you see him pick up the ball 30 yards from our goal and end up in the opposition box very quickly.
"The lad has the ability, has great pace and we probably need to develop his end product. We're getting a good character and a good talent. I'm excited to be getting the chance to work with him."