Vazquez made 33 appearances for Real in all competitions this season and scored in the penalty shootout to help his team win Saturday's Champions League final against Atletico Madrid.
“I wanted to balance the squad and I think I've chosen the best,” Del Bosque told a news conference in Salzburg on Tuesday.
Spain won the Euros in 2008 and 2012.
Real midfielder Isco was left out while team mate Dani Carvajal was excluded after the right back sustained a leg muscle injury against Atletico.
Carvajal's replacement Hector Bellerin, 21, is the youngest player in the squad.
“Bellerin is a player of the present and of the future,” Del Bosque said. “We know we can count on him.”
Uncapped midfielder Saul Niguez was omitted despite an impressive campaign for Atletico.
Goal machine Aritz Aduriz, 35, is the oldest player in the squad. He has only two caps for Spain but scored 33 goals in 44 appearances in all competitions for Athletic Bilbao this season.
“It's not normal to be playing at the Euros at my age so this is a big reward,” Aduriz said.
The Real and Atletico players will meet up with the rest of the squad on Saturday and be available for the final warm-up game against Georgia in Getafe on June 7.
Spain meet South Korea in a friendly in Salzburg on Wednesday.
The holders begin their Euro campaign against Czech Republic in Toulouse on June 13. They also face Turkey and Croatia in Group D.
Goalkeepers: Iker Casillas (Porto), David de Gea (Manchester United), Sergio Rico (Sevilla)
Defenders: Marc Bartra (Barcelona), Jordi Alba (Barcelona), Gerard Pique (Barcelona), Cesar Azpilicueta (Chelsea), Hector Bellerin (Arsenal), Sergio Ramos (Real Madrid), Juanfran (Atletico Madrid)
Midfielders: Sergio Busquets (Barcelona), Mikel San Jose (Athletic Bilbao), Cesc Fabregas (Chelsea), Thiago Alcantara (Bayern Munich), Bruno Soriano (Villarreal), Andres Iniesta (Barcelona), Koke (Atletico Madrid)
Forwards: Pedro (Chelsea), David Silva (Manchester City), Alvaro Morata (Juventus), Aritz Aduriz (Athletic Bilbao), Nolito (Celta Vigo), Lucas Vazquez (Real Madrid).
Original source: Spain name uncapped Vazquez in Euro squad