Costa's place in the 23-man party has been a point of contention, with Chelsea manager Jose Mourinho suggesting the 25-year-old striker would benefit from a period of rest during the international break.
The Brazil-born forward has started life in the Premier League in exceptional form, scoring eight goals in six league appearances, but he has been carrying a hamstring injury in the early stages of the season.
However, Spain boss Del Bosque has risked the wrath of Mourinho and insists he had no hesitation in selecting Costa, stating: "If we bring in Costa it is because he is good. He is playing all the matches."
Costa is yet to score for Spain in five appearances and his place in the starting XI for the Group C matches could come under threat from Valencia's Paco Alcacer, who scored on his first Spain start in the 5-1 drubbing of Macedonia last month.
Alcacer is joined in the squad by club-mate Rodrigo, who could make his Spain debut.
Bayern Munich left-back Juan Bernat, who joined from Valencia in the close-season, is also in line to make his international bow.
"The performances of Rodrigo and Bernat are good," Del Bosque added. "They should be players for many years in the Spain team."
Spain face Slovakia in Zilina on October 9, before heading to Luxembourg three days later.
Squad in full:
Goalkeepers: Kiko Casilla (Espanyol), Iker Casillas (Real Madrid), David de Gea (Manchester United),
Defenders: Jordi Alba (Barcelona), Raul Albiol (Napoli), Cesar Azpilicueta (Chelsea), Juan Bernat (Bayern Munich), Dani Carvajal (Real Madrid), Juanfran (Atletico Madrid), Gerard Pique (Barcelona), Sergio Ramos (Real Madrid)
Midfielders: Sergio Busquets (Barcelona), Santi Cazorla (Arsenal), Cesc Fabregas (Chelsea), Raul Garcia (Atletico Madrid), Andres Iniesta (Barcelona), Ander Iturraspe (Athletic Bilbao), Koke (Atletico Madrid), Pedro (Barcelona), David Silva (Manchester City)
Forwards: Paco Alcacer (Valencia), Diego Costa (Chelsea), Rodrigo (Valencia)
