The Portugal star, who scored twice in the 3-0 win over Hungary on matchday one and then once against Germany, is the first player in history to reach 20 goals across both competitions.
The 36-year-old overtook former Germany striker Miroslav Klose, who managed 19 goals over his career at the two tournaments.
Ronaldo this year became the first player to appear at five different European Championships, having made his tournament debut back in 2004.
He is the leading goalscorer at the event with 13, four more than previous record-holder Michel Platini, and he has made the most appearances at the Euros and World Cup (41).
Ronaldo's goal in Budapest also ended his barren run against France. He had never previously scored against Les Bleus in six appearances, making the world champions the international opponents he had faced most often without netting.