Page has paid with his job after poor performances in friendlies against Gibraltar and Slovakia. Failure to reach Euro 2024 set Page's fate.
Dave Adams, the FAW's chief football officer, said: “I would like to thank Rob for his work with the association over the last seven years, firstly as the under-21s head coach and then onto the role of Cymru (Wales) head coach."
FAW chief executive Noel Mooney said: "On behalf of myself and the entire FAW, I extend our heartfelt gratitude to Rob for his commitment and dedication to his roles for the national teams.
"Under Rob Page's leadership, our Cymru men's team has achieved significant milestones and victories which have created many incredible memories for our nation, most notably our first World Cup in 64 years."