The Gunners star missed most of last season after picking up an ankle injury and missed England's Euro 2012 campaign.
Emmanuel Frimpong, who suffered a cruciate ligament injury whilst on loan at Wolves last season, has also returned to first-team training.
Arsene Wenger said: “We are so pleased that Jack is back in full training. It’s been 14 months and that’s a long time for someone at his age. It’s an eternity, but it’s great news.
"We have to give him a few training sessions to see how he copes and responds to it. That’s the delicate, sensitive stage - to choose when to bring him in and out. We’ll have to handle that day-by-day.
"We also have Emmanuel Frimpong who has returned to full training this week, which is great news as well. Emmanuel has also been out a long time, but is progressing well.”