Costa moved to Europe in 2005, signing first with Portuguese club Penafiel and then moving around Spain with spells at Celta Vigo, Valladolid, Rayo Vallecano and now Atletico Madrid.
He has scored 17 goals in 18 games for Atletico this season. That reliability makes Costa an interesting alternative for Spain to Fernando Torres, who is so erratic with Chelsea.
The 23-year-old Costa also has a gritty streak not found in all of Spain's players.
"Diego has a particular character that makes up a big part of his game," Senna said.
Costa played a few minutes for Brazil in friendlies against Russia and Italy in March but never in an official competitive match, leaving him eligible for Spain.
A leg muscle injury prevented him from making his debut for Spain on Saturday against Equatorial Guinea. His next chance will come on March 5 when Spain plays an international friendly against Italy.
Costa said making himself available to Spain was his way of repaying the country where he's been successful as a professional.
"It's a complicated decision because it's a decision related to the country where you were born against the country that has given you everything," he said. "I hope people can understand and respect this decision, which was very difficult to take."
Senna said choosing to play for Spain was "the easiest decision of my life."
He was the 40th naturalized player to do so.
"From the very first minute, you feel like a privileged person to be pulling on the jersey," said Senna, who spent 11 seasons at Villarreal. "It's reciprocal. You want to thank the people with your on-field play for all the care and attention they show you."
Brazil coach Luiz Felipe Scolari was among those critical of Costa's choice. He accused him of turning his back "on the dream of millions, to represent the five-time world champions in a World Cup in Brazil."
Spain coach Vicente del Bosque has been welcoming.
"Nobody chooses where they are born," Del Bosque said. "The national team is not a closed club, everyone will be well received here."
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