The Iran international - who featured in all three of his country's matches at the World Cup - is determined to force his way into Chris Hughton's first-team plans.
The 24-year-old has signed a five-year contract until June 2023, and becomes Brighton's eighth major signing of the summer transfer window.
Jahanbakhsh scored 21 goals and recorded 12 assists in the Eredivisie last season as AZ finished third behind PSV and Ajax.
Brighton is paying in the region of a record club £17m for Jahanbakhsh.
Leicester City and West Bromwich Albion had also shown interest in signing Jahanbakhsh.