He had been admitted to hospital this week with coronavirus-like symptoms, the pandemic having sent Spain and other nations into lockdown.
Sanz's son, Lorenzo, on Saturday, confirmed his father's passing on Twitter before LaLiga and Madrid released statements.
"My father has just died," he wrote. "He did not deserve it to end in this manner. One of the best, most courageous and hard-working people I have seen in my life. His family and Real Madrid were his passion."
In a statement issued on their official website, Madrid said: "Real Madrid, its president and the board of directors regret with great consternation the death of Lorenzo Sanz, who was president of Real Madrid from 1995 to 2000.
"They also want to express their deepest condolences and all their affection and affection to his wife Mari Luz, their children, Lorenzo, Francisco, Fernando, María Luz [Malula] and Diana, and their family and friends. Condolences that also extend to all Real Madrid.
"Today, Real Madrid is mourning the loss of a president who dedicated a large part of his life to his great passion: Real Madrid.
"Given the current circumstances, Real Madrid will pay him the recognition he deserves as soon as possible."