In a statement on the club's website, current president Perez highlighted the success Madrid enjoyed under Sanz, who presided over two Champions League triumphs, including the 1998 title that ended a 32-year wait for glory in Europe's top club competition.
"Today, we remember Lorenzo Sanz, who has fallen victim to this tragedy," Perez said.
Statement by president Florentino Pérez on Lorenzo Sanz.#RealMadrid— Real Madrid C.F. 🇬🇧🇺🇸 (@realmadriden) March 22, 2020
"He was the president who gave us Madridistas the long-awaited European Cup after a 32-year absence. We Madridistas will forever remember him as the president who brought hope and joy flooding back on the 20th of May 1998 in Amsterdam.
"La Septima was ours. It was then followed by La Octava two years on, in the year 2000 in Paris, as Real Madrid returned to its rightful position in football's history books.
"Beyond those two European Cups, under his tutelage, the club also clinched one Intercontinental Cup, one LaLiga title, a Spanish Super Cup, a basketball league title and Cup Winners' Cup."
Perez said Sanz still attended Madrid matches regularly and was present to witness the club's four Champions League triumphs between 2015 and 2018.
He had been admitted to hospital with coronavirus-like symptoms and his son, Lorenzo, announced his death on social media on Saturday.
Perez added: "We've lost a fine Madridista who dedicated a large part of his life to what was both his and his family's greatest pleasure: Real Madrid.
"Here at the club, we'll do all we can to honour his memory and legacy, to pay him the tribute that all of Madridismo craves. Lorenzo deserves the greatest recognition.
"A tribute to him in our Santiago Bernabeu Stadium, where he continued to attend every game in order to stay close to his team. For now, as we all know, this is not possible, but we will of course ensure it takes place in order to enshrine his memory in the minds of new generations of Madridismo."