Jonker will remain at Wolfsburg until the end of the season before succeeding current head of youth development Liam Brady on July 1.
Jonker spent seven years working with the youth set-up of the Dutch Football Association, and Arsenal chief executive Ivan Gazidis expressed his delight at having secured the services of the 51-year-old.
"Youth development is a key part of our philosophy at Arsenal and I am delighted that Andries is joining us," Gazidis told the club's official website.
"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 are currently top of the Premier League table, one point clear of Manchester City and two clear of Chelsea.