Sanz was in charge of the Spanish giants from 1995-2000, overseeing two Champions League titles.
“My father has just passed away. He did not deserve this ending and in this way,” tweeted his son, Lorenzo Sanz junior.
“One of the best, bravest and hardest-working people I have ever seen. His family and Real Madrid were his passions.”
Three days ago, Sanz Jr., a former professional basketball player, said that his father had been admitted to a Madrid hospital after suffering the symptoms of the coronavirus which has killed more than 1,381 people in Spain.
Sanz claimed a place on the Real Madrid board in the mid-1980s, when the president was Ramon Mendoza.
He replaced Mendoza as president in 1995.
With Jupp Heynckes as coach and star players such as Davor Suker, Roberto Carlos, Clarence Seedorf, Fernando Hierro and Raul, Real won the Champions League in 1998 by beating Juventus in the final.
It was their seventh European Cup but first in 32 years.
Two years later, in Paris, Real claimed an eighth by beating Valencia in the final.
However, that same year, Sanz was ousted as president by Florentino Perez, who opened a new era at the club, adding five more Champions Leagues in two decades.
Current club captain and Spanish international Sergio Ramos, who with teammates is in quarantine after one of the club’s basketball players tested positive for the virus, hailed Sanz.
“Very sad day for Real Madrid. Lorenzo Sanz connected yesterday and today with two numbers for history - 7 and 8,” tweeted Ramos in reference to the key Champions League titles.
“His death saddens us even more in these difficult days in which we find ourselves. My deep condolences to his family and friends. Rest in peace.”