The 20-year-old had become a regular for the London club and forced his way into the England side before being struck down.
"We are so pleased 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," manager Arsene Wenger told the club website.
"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."
Fellow midfielder Emmanuel Frimpong has also resumed full training after injuring his cruciate ligaments when on loan at Wolverhampton Wanderers in February.
Both Wilshere and Frimpong will face a battle to return to the first team after Wenger drafted in Spain midfielder Santi Cazorla and Arsenal made a decent start to the Premier League season, lying third after four games.