The 20-year-old will stay on a season-long loan at QPR.
“Jay is a fine young player, who will prove to be a quality addition to the squad,” manager Jim Magilton told the club’s official website.
“He’s already shown glimpses of his quality at Arsenal and during loan spells elsewhere, and we’ll be looking for him to continue his progression under our guidance.
“There’s no doubt he’s got all the attributes to be a top, top player, but he needs games, and we’re delighted we’ve been given the opportunity by Arsenal to provide him with a platform to showcase his ability.”