Having previously come on as a substitute in two friendlies for Brazil last March - the first against Italy - Costa received Spanish nationality and made the controversial decision to switch allegiances.
The Atletico Madrid striker, who boasts 21 La Liga goals this season, is now in line to represent Spain for the first time, having been included in the defending world champions' squad to face Italy.
Coach Vicente del Bosque said of Costa: "He's an unusual case, because he had never been called up before and because he was born in Brazil.
"But he's a player who has been called up on the back of what he has achieved with his club and because we believe that he can help us. That's why we've called him up; for no other reason."
Italy can be expected to pose a stern test of Spain's FIFA World Cup credentials and the two sides are familiar with each other, having met four times inside the last three years.
Spain's only defeat during that time came in a friendly in August 2011.
Del Bosque's men then drew with Italy in Group C of the UEFA European Championships a year later before running out 4-0 winners against the same opponents in the final of the competition.
Spain needed penalties to see off Italy again in the FIFA Confederations Cup semi-finals last year following a goalless draw.
With Del Bosque set to name his squad for the 2014 World Cup on May 25 - four days ahead of a friendly with Bolivia - this week's game against Italy could represent the last chance for Spain's fringe players to nail down a place.
Italy, meanwhile, have drawn both of their friendlies - against Germany and Nigeria - since qualifying for the finals and have fixtures with the Republic of Ireland and Luxembourg pencilled in before a World Cup opener against England in Manaus.
Roma midfielder Danielle De Rossi has been left out by national coach Prandelli after throwing a punch at Mauro Icardi during Saturday's goalless draw with Inter.
Striker Mario Balotelli is also absent with a shoulder problem, but uncapped Torino striker Ciro Immobile could feature after scoring 13 Serie A goals this season.
Both sides were unbeaten in qualifying and topped their respective groups, although Spain's last two outings have been less than convincing.
Spain narrowly beat Equitorial Guinea 2-1 in November before going down 1-0 to South Africa three days later.
