Silva, 32, won the 2010 World Cup and 2008 and 2012 European Championship titles and played 125 times for Spain after making his debut in 2006.
He said he was “very proud” of his achievements with La Roja, and that the decision to retire was “one the most difficult of my career”.
Aragones led Spain to their first major trophy at an international tournament in 44 years with victory in the 2008 Euros. He died at the age of 75 in 2014.
On Saturday, Barcelona’s 31-year-old centre-back Gerard Pique also confirmed his retirement from the international game.