Under Williams' stewardship the team won the Formula One drivers' title seven times and the constructors' championship on nine occasions.
A statement from Williams Racing read: "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."
The team statement continued: "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.
"For those wishing to pay tribute, we ask that donations are made in place of gifts to the Spinal Injuries Association, alternatively we would welcome flowers to be placed at the entrance of the team's headquarters in Grove, Oxfordshire.
"Details of the memorial service will follow in due course."
Williams driver George Russell paid his own tribute on Twitter.
He wrote: "Today, we say goodbye to the man who defined our team. Sir Frank was such a genuinely wonderful human being and I'll always remember the laughs we shared.
"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."
Stefano Domenicali, chief executive of F1 rights holders the Formula One Group and former Ferrari team principal, described Williams as a "true giant" of the sport.
Domenicali said in a statement: "This morning Claire Williams called to inform me of the very sad news that her beloved father, Sir Frank Williams had passed away.
"He was a true giant of our sport that 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 their friends at this sad time."
The Williams team enjoyed their first F1 race win at the 1979 British Grand Prix at Silverstone with Clay Regazzoni at the wheel.
In 1980, Australian Alan Jones steered the team to the drivers' and constructors' titles for the first time.
The team’s most recent F1 success came in the 1997 drivers championship with Jacques Villeneuve and also won the constructors’ championship the same year, repeating the double 12 months after doing the same with Damon Hill taking the title.
In 1994, Williams was charged with manslaughter following the death of Ayrton Senna in a crash at Imola but was acquitted several years later.
He ceased to have any involvement with the team following its sale in 2020 and his daughter Claire quit her post as deputy team principal later the same year.