Garry Whyte, 26, was taking part in a race round the circuit when he suffered fatal injuries.
He hit his head after his pre-1930 GN Gnome single seater car rolled over halfway through the GP Itala Trophy Race organised by the Vintage Sports-Car Club (VSCC).
He was airlifted to hospital in Coventry following the accident on April 12 in which no other cars were involved, but passed away in hospital six days later having succumbed to his injuries.
Mr Whyte, an engineer, of Giffnock, near Glasgow, had been involved in races across the country for around two-and-a-half years.
His death has left his father Duncan, 59, mother Linda, 55, brother Allan, 29, and sister Katie, 27, devastated.
In an online tribute, Allan Whyte said: "My wee brother's death is the worst thing that has ever happened to my family."
Mr Whyte's funeral service will be held at Merrylea Parish Church in Newlands, Glasgow, and the city's Linn Crematorium next Tuesday.
His family have asked for donations to be made to the Headway charity.
The accident happened during the Spring Start meeting, which was the VSCC's first of this season.
James Taylor, of the VSCC, said: "Garry was a lovely guy who had become a very popular figure in the paddock at our events."