The 51-year-old is currently an assistant coach at Wolfsburg but will succeed Liam Brady, who is stepping down from his role, at the end of the season.
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Jonker has previous experience of coaching youngsters during 10 years, over two spells, at the Dutch football association, and has been Louis van Gaal's assistant at Barcelona and Bayern Munich.
"I am very pleased that Andries is joining us," Arsene Wenger told the club’s official website.
"He has a big reputation in the game and was a key part of the team which developed the structures which are now producing such strong young players in Holland. I look forward to working with him.
"I would also like to thank Liam for his work which has been outstanding over many years."
Chief executive Ivan Gazidis added: "Youth development is a key part of our philosophy at Arsenal and I am delighted that Andries is joining us.
"He has an outstanding track record in developing and identifying young players and creating systems to bring the best out of them.
"I know he will build on the tremendous work which has been done by Liam and his team over many years."
Arsenal confirmed that Brady will remain associated with the club in ambassadorial role.