Van Basten, 49, will leave Heerenveen at the end of the season and take charge of Alkmaar on a two-year contract.
A statement on AZ's website read: "AZ and Marco van Basten have reached a verbal agreement on a contract as head coach until the summer of 2016. The 49-year-old will succeed Dick Advocaat.
"The last formalities will be completed in the next few days, after which the Utrecht-born coach can be presented."
Alkmaar are currently seventh in the Eredivisie table, while Heerenveen are five points better off in sixth.