Koeman embarked on a summer policy of reducing the wage bill and de Cler was the latest individual to leave the Amsterdam ArenA.
The completion of the three-year deal will come as a relief to de Cler, who saw a move to West Brom fail to materialise following a trial at the Hawthorns earlier in the summer.
The 23-year-old was a regular starter under former Ajax coach Co Adriaanse, but Koeman deemed him surplus to requirements and AZ stepped in to offer him a deal before the August 31 transfer deadline.
