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Wolfsburg finished fourth in the Bundesliga last season, Glasner's second at the club, to reach the Champions League group stage for the third time in their history, and first occasion since 2015-2016.
Van Bommel's only previous managerial job came when he spent 18 months with PSV between 2018 and 2019.
He has also worked in support of Bert van Marwijk, his father-in-law, holding assistant roles with Netherlands, Australia, Saudi Arabia and United Arab Emirates at international level.
Van Bommel spent five years of his playing career in the Bundesliga with Bayern, with whom he won two top-flight titles.
Van Bommel told his new club's website: "I'm really looking forward to working for Wolfsburg and I'm excited about my new environment, the people and the task that awaits me.
"The ideas of those responsible are identical to my view and I can identify very well with the path the club has taken.
"Being able to work as a coach in the Bundesliga, in which I have played for so long, is a great honour and challenge for me, which I will tackle together with everyone involved with a lot of joy and great commitment."