He died of a suspected heart attack and was found in his house on the French Riviera by a friend on Sunday.
Button's F1 team McLaren today confirmed the sad news and team principal Martin Whitmarsh said: "In my long Formula 1 career, I've encountered many drivers' fathers, but I think it's safe to say that John was perhaps more devoted to his son than any of them."
British driver Max Chilton of Marussia tweeted: "So sad and shocked to hear the sad passing of John Button. One of the greatest characters in the paddock & will miss him dearly. #RIP"
My condolences to all the Button family, especially to Jenson . Very sad news. John....a great man, a friend, we will miss him.— Fernando Alonso (@alo_oficial) January 13, 2014
"I'm very very sorry for my teammate, @JensonButton. His dad was a really great guy who will be missed by all in #F1. #JohnButtonRIP," tweeted new McLaren driver Kevin Magnussen.