Ajax suffered a woeful season by their own standards which saw the club fail to qualify for the Champions League for the first time in 13 seasons.
Steijn made his mark last year as he led modest Sparta Rotterdam to a sixth place finish in the Eredivisie -- the team's best result in 27 years.
Despite that achievement, the 49-year-old's appointment to the club who have won a record 36 Dutch league titles came as a surprise as he has spent most of his 12-year coaching career at smaller Dutch teams.
"He has outperformed at every club where he has worked," Ajax football director Sven Mislintat said in a statement. "I am convinced he is ready to make the step up."
Ajax dismissed coach John Heitinga earlier this month after finishing third in the standings, 13 points behind champions Feyenoord.