The 48-year-old was signed last year to coach the Ajax reserve team who compete in the second tier of Dutch football and finished the season as runners-up,
Keizer has been handed a two-year contract with the senior squad.
He coached previously at SC Cambuur, where he also spent most of a playing career that started with four appearances for Ajax’s first team in the 1987-88 season.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Bosz departed after one season in charge to take over at Germany's Borussia Dortmund having taken Ajax to the Europa League final, which they lost 2-0 to Manchester United, and second place in the Dutch league behind Feyenoord.
(Reporting by Mark Gleeson, editing by Ed Osmond)
