Williams was born on 16 April 1942 in South Shields, County Durham, the son of a Royal Air Force officer. After his parents separated he was partly raised by an aunt and uncle in Jarrow before attending St Joseph's College boarding school in Dumfries, Scotland. His interest in motor racing was sparked in the late 1950s when a friend gave him a ride in a Jaguar XK150.
After a brief career as a driver and mechanic, Williams founded Frank Williams Racing Cars in 1966, financing the operation through work as a travelling grocery salesman. The team ran cars in Formula Two and Formula Three, and one of its earliest significant relationships was with driver Piers Courage.
Williams entered Formula One in 1969, purchasing a Brabham BT26 chassis for Courage to drive. The season yielded two second-place finishes, at Monaco and Watkins Glen, signalling genuine competitiveness on a modest budget. The following year Williams entered a partnership with Alejandro de Tomaso and switched to a De Tomaso chassis, but the arrangement ended in tragedy when Courage was killed in a fiery accident at the 1970 Dutch Grand Prix.
Williams pressed on through difficult financial circumstances, at one point conducting team business from a public telephone box after being disconnected for unpaid bills. He ran Henri Pescarolo in 1971 with a March chassis, and in 1972 produced the Politoys FX3, the first Formula One car built by the Williams works, designed by Len Bailey; it was destroyed at its debut when Pescarolo crashed. A sponsorship arrangement with Iso Rivolta followed before Williams brought in Walter Wolf as a partner in 1976. When the team effectively ceased to belong to Williams, he departed in 1977.
Together with engineer Patrick Head, Williams acquired a disused carpet warehouse in Didcot, Oxfordshire, and established Williams Grand Prix Engineering. The new team's early signings included Neil Oatley as a draughtsman and Frank Dernie, formerly of Hesketh Racing, who contributed knowledge in aerodynamics and suspension geometry.
The team's first Grand Prix victory came when Clay Regazzoni drove the Cosworth-powered Williams FW07 to win the 1979 British Grand Prix at Silverstone. Success accelerated rapidly: Alan Jones won the Drivers' Championship in 1980, the team's first, alongside the first of nine Constructors' titles. Between 1980 and 1997, Williams drivers including Keke Rosberg, Nelson Piquet, Nigel Mansell, Alain Prost, Damon Hill, and Jacques Villeneuve won six further Drivers' Championships. The team accumulated 114 Grand Prix victories.
The darkest moment of the competitive era came in May 1994 when Ayrton Senna died at the wheel of the Williams FW16 at Imola. Williams was charged with manslaughter under Italian law but was acquitted in 1997. From the 1995 FW17 onward, every Williams chassis carried a small Senna logo on its front wing supports as a permanent tribute.
Williams met Virginia Berry in 1967 and married her in 1974. They had three children: sons Jonathan and Jaime, and daughter Claire, who later became deputy team principal of Williams Grand Prix Engineering.
On 8 March 1986, while driving with team sponsorship manager Peter Windsor from the Paul Ricard Circuit to Nice airport, Williams lost control of a hired Ford Sierra on a slight left-hand kink in the road. The car clipped a low stone wall and dropped eight feet into a field, rolling onto the driver's side. Williams suffered a spinal fracture between the fourth and fifth vertebra and was left tetraplegic. Windsor, who sustained minor injuries, extracted Williams from the vehicle. An emergency tracheotomy at Royal London Hospital drained fluid from his lungs and almost certainly saved his life.
Williams subsequently required full-time care but remained as team principal, continuing to attend races and direct the team from his wheelchair. His wife Virginia wrote about the experience in her 1991 book A Different Kind of Life. She was diagnosed with cancer in 2010 and died on 7 March 2013, aged 66.
In March 2012 Williams announced he would step down from the board, with Claire Williams taking over his directorial role, though he remained team principal. He ceased involvement when the team was sold to Dorilton Capital in September 2020.
Williams was admitted to hospital in Frimley, Surrey on 26 November 2021 and died on 28 November 2021, aged 79.
Williams was appointed Commander of the Order of the British Empire in the 1987 New Year Honours and received a knighthood in the 1999 New Year Honours for services to the motor sport industry. France appointed him a Knight of the Legion of Honour for his work with Renault engines. He received the Wheatcroft Trophy in 2008 and the BBC Sports Personality Helen Rollason Award in 2010. Williams was inducted into the Motor Sport Hall of Fame in 2011 and a road in Didcot was named Sir Frank Williams Avenue in 2012.