Born in South Shields, Tyne and Wear, England, to an RAF officer and a special education teacher and later headmaster, Williams was largely brought up by his maternal aunt and uncle in South Shields when his parents' marriage broke down. He subsequently spent much of his later childhood at a boarding school, St. Joseph's College, Dumfries, in Scotland. In the late 1950s a friend gave Williams a ride in his Jaguar XK150 and young Frank was immediately hooked.
After a brief career as a driver and mechanic, funded by his work as a traveling grocery salesman, Williams founded Frank Williams Racing Cars in 1966. He ran drivers including Piers Courage and Tony Trimmer for several years in Formula Two and Formula Three. Williams purchased an old Brabham Formula One chassis which Courage drove in several F1 events, coming in second place twice.
In 1970 Williams undertook a brief partnership with Alessandro de Tomaso. After the death of Courage at the Dutch Grand Prix that year, Williams' relationship with de Tomaso was ended. In 1971 he raced Henri Pescarolo in a chassis he had purchased from March Engineering. 1972 saw the first F1 car built by the Williams works, the Politoys FX3 designed by Len Bailey, but Pescarolo crashed and destroyed it at its first race.
Williams, short on cash (he conducted team business from a telephone box at one point after being disconnected for unpaid bills), looked to Marlboro and Iso Rivolta, an Italian car company, for sponsorship. Though they pledged their support, they did not come through in time and in 1976 Williams desperately took on a partner, oil magnate Walter Wolf. Though the team continued functioning, it no longer belonged to Frank Williams, so he left in 1977 along with one of his old employees, engineer Patrick Head. The two acquired an empty carpet warehouse in Didcot, Oxfordshire, United Kingdom and announced the formation of Williams Grand Prix Engineering. This same team and partnership still competes in Formula One and is known as AT&T Williams F1 Team. Their first win came in 1979 from Clay Regazzoni, the first title in 1980 with Alan Jones, and a second championship in 1982 with Keke Rosberg.
A car accident in March 1986 in France left him paralyzed. While driving a rental car from the Paul Ricard Circuit to the Nice airport Williams lost control and the car rolled over causing Williams, who may not have been wearing a seatbelt, to crash into the roof causing a spinal fracture. Peter Windsor, Williams' passenger, sustained only minor injuries. Since the accident Williams has been confined to a wheelchair.
In 1987 the Queen awarded Williams the title of CBE. He was knighted in 1999. He is also one of the few non-Frenchmen to have been made a Chevalier of France's Legion d'honneur, this honour accorded for his work with Renault engines. In 2008 Williams was awarded the Wheatcroft trophy.