Ten Hag will head to Old Trafford at the end of the season, having seen his Ajax team wrap up the Eredivisie title on Thursday (AEST) with a 5-0 rout of Heerenveen.
Ajax on Thursday confirmed Ten Hag's replacement, announcing they have reached an agreement with Club Brugge boss Schreuder.
Response from Schreuder & @VdSar1970 ↓— AFC Ajax (@AFCAjax) May 12, 2022
• 'Becoming head coach at Ajax is an honor'
• 'We know Alfred as a strong coach'
The 49-year-old, who served as Ten Hag's assistant in 2018-19, when Ajax reached the Champions League semi-finals, has signed a two-year deal with an option for a third.
Schreuder only joined Belgian side Brugge in January, and is hoping to lead it to glory in the play-offs for the Belgian championship.
He coached Hoffenheim in 2019-2020, though left in June of that season and linked up with Ronald Koeman at Barcelona, acting as assistant to the former Netherlands boss, who will take charge of the Dutch giants once again following the World Cup later this year.
"Becoming head coach at Ajax is an honour and a great opportunity, that I will grab with both hands," Schreuder said.
"I'm also excited to return here, because I enjoyed the one and a half years I've worked at Ajax very much. I wish to win prizes here in Amsterdam, with a team that plays attractive football. With a good balance between experienced top players and very big talents.
"But first I want to end the season with Club Brugge successfully. I want to say goodbye with a title, that is very important to me and I will do my absolute best to accomplish that."
Ajax chief executive Edwin van der Sar added: "We know Alfred as a tactically strong trainer with good and versatile exercise material. These last years he has gained experience as a head coach and as assistant coach at top clubs in various countries and competitions."