Santos' side was not among the favourites to lift the Henri Delaunay Trophy, and earned few admirers through the tournament as it drew its three group games.
Only Wales was beaten in 90 minutes by Cristiano Ronaldo and company as the Selecao scrapped its way to a final showdown against host France.
Eder was the unlikely hero in extra time at the Stade de France after Ronaldo had been withdrawn through injury.
The tournament top-scorers, France was unable to break through Santos' resolute backline with Real Madrid defender Pepe picking up Man-of-the-Match honours.
A statement from the Portuguese Football Federation (FPF) confirmed: "The new deal between the FPF and Fernando Santos will be in force until Euro 2020, coinciding with the end of the mandate of the current Director of the Portuguese Football Federation."
Santos took charge of the national team after its group-stage elimination at the 2014 World Cup under Paulo Bento.
A Primeira Liga title in 1998-1999 with Porto, where he also won two Taca de Portugal crowns, ranked as the highest accolade in Santos' career before his EURO 2016 triumph.