The Atalanta midfielder suffered an undisclosed muscle injury two weeks ago in the final, which his club lost 1-0 to Juventus, and will not be fit in time for the tournament in Germany.
It meant he missed last Wednesday's Europa League final in Dublin, which Atalanta won 3-0 over German champions Bayer Leverkusen.
"I can't imagine I've had a week in my career, or in my life, that has had so many ups and downs. Lost the Coppa Italia, couldn't play the final, win the Europa League," De Roon posted on social media on Monday.
"In that last euphoric state, I spent a lot of time with the medical staff: it turns out I can't play the Euros.
"I will get over it, I will watch the squad and my friends as a fan, but for now it's a very tough day."
De Roon has won 42 caps for the Netherlands, competing in the last Euros and the World Cup in Qatar.
Dutch coach Ronald Koeman will announce the final Euro 2024 selection on Wednesday. After De Roon's withdrawal, the pre-selection consists of 29 players, with three set to be axed from the final squad.
The squad assembled on Monday for their first session with Quinten Timber training apart from the rest as the Feyenoord midfielder is still nursing an injury.
In the run-up to the tournament in Germany, the Dutch will play warm-up matches against Canada and Iceland next week.