Page spent four years in charge, having initially been given the role on an interim basis in November 2020.
He was then appointed permanently in September 2022 and oversaw the team at two major tournaments.
The 49-year-old took Wales to Euro 2020 and the World Cup in 2022, which was their first appearance at the tournament since 1958.
More recently, Page’s position came under review following disappointing friendly results against Gibraltar and Slovakia in June.