The New York City FC striker arrived at the national team's training ground in Las Rozas, Madrid, on Monday afternoon and was greeted with hugs from his teammates.
Chelsea forward Alvaro Morata and Barcelona defender Gerard Pique were among those players to welcome back Spain's all-time leading goal scorer.
"I'm nervous, or rather excited with this new call-up, especially after three years," Villa is quoted as saying by AS. "It's a dream come true.
"For the time being, I will be here for two games and we will see what happens afterwards. I'm ready to help the team, be one of them and I hope I get my working clothes on and help as I've always done."
Villa last played for Spain at the 2014 World Cup in Brazil, a 3-0 triumph over Australia in the final group-stage game which saw him score his 59th goal in his 97th appearance since making his international debut on February 2005.
Spain coach Julen Lopetegui had been following the former Valencia and Barcelona star for some time after his impressive form in Major League Soccer and said the call-up was "well deserved."
Villa, named MLS' MVP for the 2016 campaign, has 19 goals and four assists in 24 league appearances this season.
"For me, the fact that the national coach came to New York to see me play already gives me pride," he said. "I had spoken to him but I was surprised by the call-up. To be here for me is something that fills me with pride."
The 35-year-old added it was "a dream come true" to return to the fold.
He travelled to Spain ahead of schedule, arriving in Madrid on Friday to train over the weekend with a national team physio to get ready.
"I want to be in the best possible condition because nothing gives me more emotion than wearing my country's jersey," Villa said.
Spain captain Sergio Ramos was thrilled to have Villa, a 2008 European Championship winner and 2010 World Cup winner, back in the squad.
He said: "I experienced the best times that I've had in the national team with David so as soon as I found out about his return, I congratulated him."
Villa says he did not anticipate the welcome he has received.
"I didn't expect so many people to be happy with my return," he said. "Everyone's reaction, that of the press, of everybody... I expected more controversy but it's been fantastic. I'm here and I want to enjoy it. I still cannot believe it. I want to show everyone that I'm very eager."
Heading into Saturday's top-of-the-table clash with Italy at the Santiago Bernabeu, Spain lead Group G on goal difference with four games remaining. Spain then travel to Vaduz to face Liechtenstein on Sept. 5.
"We haven't qualified yet and we have to get the job done," Villa said. "The only important thing is to add six points in the next two qualifying games because the aim is the World Cup in Russia."
Lopetegui has been forced to make a change to the squad with Real Madrid's Lucas Vazquez replacing injured Las Palmas winger Vitolo. The former Sevilla man strained a knee ligament during Sunday's training session with his club.
Villa: Amazing to receive Spain call-up
David Villa chats with ESPN FC's Julie Stewart-Binks about NYCFC's draw at New York Red Bulls and his Spain call-up.