In a statement, the Williams team said: “It is with great sadness that on behalf of the Williams family, the team can confirm the death of Sir Frank Williams CBE, founder and former team principal of Williams Racing, at the age of 79.
“After being admitted into hospital on Friday, Sir Frank passed away peacefully this morning surrounded by his family.
“Today we pay tribute to our much loved and inspirational figurehead. Frank will be sorely missed. We request that all friends and colleagues respect the Williams family’s wishes for privacy at this time.”
Williams was a wheelchair user after suffering a spinal cord injury in a car crash in France in 1986.
F1 president and chief executive Stefano Domenicali paid tribute to Williams, whom he described as “a true giant of our sport”.
Domenicali added: “He overcame the most difficult of challenges in life and battled every day to win on and off the track. We have lost a much loved and respected member of the F1 family and he will be hugely missed.
“His incredible achievements and personality will be etched on our sport forever. My thoughts are with all the Williams family and friends at this sad time.”
Current Williams drivers George Russell and Nicholas Latifi also paid their respects.
“Sir Frank was such a genuinely wonderful human being and I’ll always remember the laughs we shared,” said Russell.
“He was more than a boss, he was a mentor and a friend to everybody who joined the Williams Racing family and so many others.”
Canadian Latifi added: “RIP Sir Frank Williams. Such sad news. A huge loss for our sport and our team.
“It’s been an honour to represent your name on the world stage and we will continue to push hard to take the team back up the grid.”