The Williams F1 team, founded in 1977, dominated under his guidance in the 1980s and 1990s, with a total of 117 racing victories.
The team, formed under his name, grew into one of the most successful in the sport, winning seven driving titles and nine Constructors Championships.
“After being admitted to hospital on Friday, Sir Frank passed away peacefully this morning surrounded by his family.
“Today we pay tribute to the much-loved and inspiring leader. Frank will be greatly missed. At this time we urge all friends and colleagues to respect the privacy choices of the Williams family.”
Williams suffered a spinal cord injury in a 1986 car accident that left him unable to walk.
He left the Williams team in 2012 and handed over the team’s daily run to his daughter Claire in 2013.
Williams and his family have sold the group to investment firm Torilton Capital over the past 12 months.
Current Williams F1 drivers George Russell and Nicholas Latifi paid tribute to Williams on Twitter.
“It was a race that truly honored him and was just a small part of the incredible legacy he left behind. It will live forever in the heart and soul of this team. Be calm, Sir Frank. Thank you for everything.”
“It is an honor to represent your name on the world stage and we will continue to work hard to take the team back to the stage.”
Williams’ current chief executive and team chief Jost Capito paid tribute to the team’s founder.
“Sir Frank was a hero and symbol of our game. His passing marks the end of an era for our team and the Formula 1 game. He was a kind and true pioneer. Made us one of the most successful teams.
“His values, including integrity, teamwork and strict independence and determination, are the core ethics of our team, and his legacy is as much a part of the Williams family name as it is of ours at this difficult time.”
F1 President and CEO Stefano Dominicali also paid tribute.
“He was the real giant of our game, he overcame the most difficult challenges in life and fought every day to win on and off the track. We lost the most beloved and respected member of the F1 family, and he will be greatly missed.”, Dominicali said.
“His incredible achievements and personality will be etched in our game forever. My thoughts are with all of Williams’ family and friends at this sad time.”