Di Stefano passed away at the age of 88 on Monday after suffering a heart attack two days earlier.
The Argentina-born forward made his name during an 11-year spell in the Spanish capital, with his prowess in front of goal helping Real to five-straight European Cup crowns and eight La Liga titles.
Additionally, Di Stefano won the Pichichi trophy for La Liga's top scorer on five occasions and was crowned European Footballer of the Year twice in his career.
Di Stefano went on to fulfill two brief spells as Real coach, before being named honorary president in 2000.
At a media conference following the announcement of his passing, Real president Perez labelled Di Stefano as "the most important player" in the club's history.
"Today is a day of absolute sadness for Real Madrid and dare I say it the entire football world," Perez said. "Di Stefano was the most important player in the history of Real Madrid and the best footballer of all time.
"Alfredo Di Stefano is Real Madrid. He was decisive, determinant and changed the destiny of this institution.
"He was able to extend the passion for Real Madrid to all corners of the world.
"We have the obligation to tell people that didn't see it about a footballer who was capable of everything.
"It's thanks to Di Stefano that FIFA named Real Madrid the best team of the 20th century.
"Alfredo di Stefano, president of honour, Real Madrid will never forget you."
