Di Stefano, widely regarded as one of the greatest players the game has seen, died at the age of 88 on Monday following a heart attack.
The Argentine enjoyed an 11-year spell at Real, in which he helped the club win the European Cup five years in a row from 1956 to 1960, as well as eight Spanish titles.
A two-time European footballer of the year, Di Stefano scored more than 300 times in almost 400 competitive appearances for Real, with fans, former players and club officials among those leading the tributes.
"After the long goodbye to Alfredo Di Stefano at the public viewing in the Santiago Bernabeu, fans have said their final farewells," read a statement on Real's official website.
"They gave him an ovation as he left through the president's box gate. The coffin was then taken to La Almudena cemetery in Madrid for the funeral, where [president] Florentino Perez and the board of directors accompanied the family of the greatest player in history."
Perez visited the public viewing of Di Stefano's coffin on Tuesday along with first-team players Sergio Ramos, Dani Carvajal and long-serving goalkeeper Iker Casillas.
"The Bernabeu was his factory, his home and his sacred ground. It is here we will pay him the tribute he deserves," Perez told AS.
FIFA has confirmed there will be a moment of silence ahead of Argentina's semi-final with Netherlands at the World Cup on Wednesday to honour Di Stefano's achievements, while black armbands will also be worn by the players.
