The Atletico Madrid man is set to make his debut for the reigning world champions, while Juan Mata and Fernando Llorente miss out
The Atletico Madrid attacker previously represented the Selecao at international level, but can switch allegiances as he had yet to play for the Confederations Cup winners in an official game.
Del Bosque has also called up Bayern Munich defensive midfielder Thiago Alcantara for Wednesday's encounter, while his FCB team-mate Javi Martinez has also made the cut.
"This is the squad for the game against Italy and does not mean anything for the World Cup," Del Bosque stated at a press conference.
"Costa is in it because of what he has done with Atletico Madrid. Thiago has been doing very well at Bayern. He faces stiff competition in midfield there, but has become a starter.
Meanwhile, Manchester United midfielder Juan Mata and Juventus striker Fernando Llorente have both been left out, with Carles Puyol and David Villa being ignored by Del Bosque, too.
"We have a lot of respect for Llorente and really value him, like a lot of other players who didn't make it this time.
"We are not writing off Puyol. We do not have any doubts about him when he's fit and plays regularly."
Squad in full:
Goalkeepers: Casillas (Real Madrid), Reina (Napoli), Valdes (Barcelona)
Defenders: Alba (Barcelona), Albiol (Napoli), Azpilicueta (Chelsea), Juanfran (Atletico Madrid), Martinez (Bayern Munich), Ramos (Real Madrid)
Midfielders: Alonso (Real Madrid), Busquets, Fabregas, Iniesta, Xavi (All Barcelona), Cazorla (Arsenal), Koke (Atletico Madrid), Thiago (Bayern Munich)
Attackers: Costa (Atletico Madrid), Pedro (Barcelona) Navas, Negredo, Silva (All Manchester City)