Villa, Spain's all-time leading scorer, broke his left leg while competing in the Club World Cup with Barca in December, and has not played a competitive match since then.
"I tried right to the end but I wasn't able to get to 100 percent for the Euros," Villa said on his official Twitter feed.
"Today I called the coach to tell him. It was the most honest thing to do. Thanks to all of you for your support."
"After failing to achieve the desired progress in recent training sessions, Villa spoke with Del Bosque," the RFEF said.
"[He] told him although he would like to be with the team in Poland and Ukraine, his physical state 'isn't the best' for a competition like the Euros.
"The RFEF and Spain's coaching staff wish the player all the best in his recovery and hope he will return soon to the national team, and value the effort made by David to get back to full fitness."
Barcelona's Cesc Fabregas wrote: "Keep your spirits up, you are a star. You have been and will continue being the best goal-scorer in the national team."
Chelsea winger Juan Mata wrote: "You have proved again you are an example, we will miss you a lot. You will soon be back scoring goals."
Barca's doctors had already said he would not make the King's Cup final on Friday, when Pep Guardiola's side take on Athletic Bilbao.
Torres, Valencia's Roberto Soldado, Sevilla's Alvaro Negredo and Atletico Madrid's Adrian Lopez are already in the squad, while Bilbao's Fernando Llorente and possibly Barca's Pedro are expected to be called up, with others making way.
