The 49-year-old Dutchman has agreed to a two-year contract with the option to extend by an additional year.
During Schreuder's time under Ten Hag at Ajax, he held the club reach the semi-finals of the Champions League and win a league and cup double.
Therefore, the Ajax chiefs believe Schreuder is the right man to take over from Ten Hag in the summer.
Speaking about the appointment, Ajax chief Edwin van der Sar said: "We know Alfred as a tactically strong coach 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.
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