The Atletico Madrid forward will play for La Roja for the first time since announcing last year his intention to represent Spain rather than his home country, World Cup hosts Brazil.
"It was a complicated decision at the time," Costa said to Spanish TV channel Canal Plus. "But it was a choice that I gave a lot of thought to and I tried to do the right thing.
"Spain showed an interest and I felt wanted.
"If they thought that I could be important to them, considering the team they have, then it's a privilege."
Costa, who moved to Spain in 2007 after playing in Portugal, has netted 21 goals in 24 Primera Division games this season and is the second leading scorer behind Real Madrid's Cristiano Ronaldo.
The 25-year-old is taking nothing for granted when it comes to making the Spain squad this summer, however.
"(Spain coach Vicente) Del Bosque has always been crystal clear and never promised me anything," Costa said. "And this is what I like.
"I need to earn my place through work and effort.
"I would love to play at the World Cup in Brazil and do things just as well as Spain did in the last World Cup."
With 100 days to go before Spain start their title defence in South America, Wednesday's match at the Vicente Calderon will be an important test for the two sides, according to Spain midfielder Andres Iniesta.
"The games against Italy are always beautiful and special," he said. "We expect an intense game as usual against them because Italy are one of the top national teams."
Italy have not beaten Spain since a friendly in 2011.
Since then, the Spaniards have had the upper hand.
Spain held Italy to a draw in the group stages of Euro 2012 before thrashing the Azzurri 4-0 in the final of the competition.
The last time the sides met was last year in the semi-final of the Confederations Cup in Brazil, where Spain needed penalties to beat Italy.
"We will try to attack Spain, as we did in the Confederations Cup, and force the world champions to defend themselves," Azzurri coach Cesare Prandelli said. "But we expect a difficult game against a team that likes to control possession.
"I always say that if we are no longer the best, we can still beat the best."
Wednesday's game will be one of two warm-up matches for Italy before they open their World Cup campaign against England in Manaus on June 14.
Italy travel to Spain without several players, including injured AC Milan striker Mario Balotelli.
Moreover, Prandelli has left Roma midfielder Daniele De Rossi out of his squad as punishment for his violent gesture towards an opponent at the weekend.