The High Court claim brought against helicopter manufacturer Leonardo S.p.A. is valued at Stg 2.15 billion ($A4.28 billion).
Vichai and four others died in the crash just outside the Premier League team's King Power Stadium after a match in October 2018.
"My family feels the loss of my father as much today as we ever have done," said Vichai's son, Aiyawatt Srivaddhanaprabha. "That my own children, and their cousins, will never know their grandfather compounds our suffering."
An inquiry by the British government's Air Accidents Investigation Branch (AAIB) found that a damaged tail rotor led to the crash and ruled out pilot error.
"My father trusted Leonardo when he bought that helicopter but the conclusions of the report into his death show that his trust was fatally misplaced," said Aiyawatt, who succeed Vichai as chairman of Leicester.
"I hold them wholly responsible for his death."
A press release issued on Friday said the claim sought compensation for loss of earnings and other damages.
It said King Power, the company founded by Vichai, was earning revenue in excess of Stg 2.5bn ($A5.0bn) a year.
It added net profit peaked at Stg 237m ($A472m) the year before his death.
The Leonardo AW169 helicopter took off from the centre of the field at the King Power Stadium after a Premier League match.
The inquiry found it got to about 430 feet (130m) above the ground, then spun around and plummeted into a concrete step outside the stadium. It found that there was a seizure of the tail rotor duplex bearing.
Club employees Nusara Suknamai and Kaveporn Punpare, pilot Eric Swaffer and Swaffer's partner, Izabela Roza Lechowicz, were all killed in the accident.
"The foundation of the claim brought against Leonardo is the independent AAIB report released in September 2023. Considering the purview of the AAIB's mission is to report on safety and not to blame, the report was as damning a report as I have ever read," said Peter Neenan, a partner at Stewarts, the law firm representing the family.
Leonardo said it would defend the claim.
"Leonardo notes that the AAIB Final Report, released in September 2023, has not directed any Recommended Actions to Leonardo.
"The AAIB report concluded that Leonardo complied with all regulatory requirements in both the design and manufacture of the AW169.
"Leonardo meets the most modern and stringent certification and safety standards in the sector. Any further comment on the claim at this time would be premature."
