Burton, a former Gunners youth player, has been brought back to the club after Steve Bould and Neil Banfield's promotion to the first-team coaching staff following Pat Rice's retirement.
He told the club's official website: "I'm delighted and proud to be joining Arsenal as reserves and head development coach.
"Having started my career at Arsenal as a youth player, and then as a coach, I know the history, class and values of this great football club. I can't wait to get started in my new role and to meet the players and my new colleagues.
"I would like to take this opportunity to thank [Wednesday manager] Dave Jones and everyone at Sheffield Wednesday for their support and understanding.
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Arsene Wenger also commented on the appointment, stating that he is happy to have got his man.
"We are delighted that Terry Burton is joining Arsenal," said the Frenchman.
"I have known Terry for many years and he is someone who is hugely respected and highly regarded in the game.
"Terry brings with him a wealth of coaching experience and he will be a great asset for us, working with our reserves and youth development players."