Page took over as manager after former boss Ryan Giggs (48) left the team due to allegations of assault. Giggs, who has denied all charges, faces a retrial next year after a jury was unable to reach a verdict on the charges last month.
Under Page, Wales reached the last 16 at the European Championship last year while they have also qualified for the World Cup for the first time since 1958.
"There is no bigger honour than coaching your national team and I can't wait for the challenge the next four years will bring, starting with our first FIFA World Cup in 64 years," Page said in a statement.
"This is an exciting time for Welsh football and I hope we can make the country proud in November and continue our success by qualifying for more major tournaments in the future."
Wales are in Group B alongside England, Iran and the United States at the November 20th - December 18th World Cup in Qatar.
Page will first turn his attention to Wales' UEFA Nations League matches later this month. The Welsh, who are bottom of League A4, take on Belgium in Brussels (September 22nd) and Poland in Cardiff (September 25th) in their final two group games.
