Ozil had been frozen out at Fenerbahce, and had not featured for the Turkish Super Lig side since March 20 after falling out with the management over his fitness. Now his contracted is believed to have been terminated by mutual consent.
The 33-year-old joined the Turkish giants in July 2021 and played 36 matches, scoring nine goals with three assists.
Meanwhile the 30-year-old Wilshere, who announced his retirement as a player last week after battling a series of injuries, returns to the club he left in July 2018.
Wilshere, who spent some time at London Colney last season working with the club's young players, told Arsenal's official website: "It's a huge honour to have this role.
"It's no secret that I love this club. I love what we stand for and a big part of my life was spent in this academy, some of the best days of my life. This is a big opportunity for me and I'm ready.
"I'm hungry and can't wait to help these young players thrive and be the best they can be on and off the pitch.
"It's a special feeling to be part of the Arsenal family. It never left me and, even though I moved on for a few years, my heart was always still at Arsenal. I can't wait to get started and help these young players thrive with a great team around me."
Academy graduate Wilshere, who also had spells with Bolton, Bournemouth, West Ham and Aarhus, made 197 appearances for the Gunners and was part of the FA Cup-winning sides of 2014 and 2015.
Academy manager Per Mertesacker said: "Everyone knows how passionate Jack is about Arsenal. He understands what we want to achieve here and he really impressed us last year.
"He knows exactly what it takes to progress through the academy into first-team football."