"It has touched us deeply that Johan was such an inspiration to many of you," his son Jordi said in a statement on Friday.
"On behalf of my mother, sisters and the rest of the family I would like to say thank you for all the love, kind words and memories that have been shared with us, since yesterday but also over the past months," added the 42-year-old former Barcelona and Manchester United forward.
Cruyff's family said they will hold a private funeral for the three-times European footballer of the year and a public memorial will also be arranged.
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The Netherlands' friendly international against France on Friday in Amsterdam will be halted for a minute-long silence after 14 minutes in tribute to Cruyff, who wore the number 14 shirt in his playing days.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
