The Madrid Open announced the death of its honorary president on Saturday. No cause of death was given.
Santana won four major singles championships: The French Championships in 1961 and 1964, the US Championships in 1965 and Wimbledon in 1966, the same year he reached the top ranking.
He added the 1963 French doubles with Australian Roy Emerson.
Santana was inducted into the International Tennis Hall of Fame in 1984.
"It's difficult for a genius to be rewarded in tennis and Manolo was one of those few who could," Gene Scott said at the hall induction ceremony where he spoke on Santana's behalf.
"He literally invented one of the strokes that we now see in profusion — the backhand topspin lob."
Rafael Nadal joined in the flood of condolences on social media, writing in Spanish that "we will all miss you Manolo".
"You will always be one of a kind and special," Nadal wrote.
"As I have said many times in the past: a thousand thanks for what you did for our country and for opening the way for others.
"You were always my role model, a friend and someone who was close to all of us."
Two-time grand slam winner Garbine Muguruza posted a photo of her with an elderly Santana with the message thanking him for his "goodness, warmth, and for showing us the way forward."
Spain's King Felipe VI and Prime Minister Pedro Sanchez echoed the sentiments of Nadal, calling Santana a "legend".
Billie Jean King fondly recalled winning her first Wimbledon title alongside Santana's triumph there in 1966.
"We danced the 1st dance at the Ball," King tweeted.
Unlike his Davis Cup teammate Andres Gimeno, Santana turned down offers to turn professional and became one of the biggest names on the tour of the 1960s.
Santana beat the top three players to win the 1961 French title - No.3 Emerson in the quarter-finals, No.2 Rod Laver next and ultimately defending two-time champion and No.1 Nicola Pietrangeli in the final.
In 1965 he became the first European man to win the US title since 1928.
He became the first men's Wimbledon champion from Spain in 1966 and labelled that triumph the biggest of his four major singles triumphs.
"This is the one all the players want to win," he's quoted as saying on the International Tennis Hall of Fame site.
"I am very happy I did it once."
After making his Davis Cup debut at 19, he still holds Spain's records for most ties (46), and most wins in singles (69) and doubles (23).
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