Cruyff, who made his name as a forward with Ajax and Barcelona, was European footballer of the year three times.
He won three consecutive European Cups with Ajax, coached Barcelona to their first European Cup triumph in 1992 and helped the Dutch reach the 1974 World Cup final, where they were beaten 2-1 by West Germany.
The Dutch FA said: “Words can hardly to be found for this huge loss.”
It added: “The greatest Dutch footballer of all time and one of the world’s best ever. Our condolences go to his wife, family, friends and the entire football world at home and abroad. We wish everyone a lot of strength in this difficult time.”
Cruyff, who had double heart bypass surgery in 1991, was diagnosed with cancer in October 2015.