Andersson's crash occurred in a blind corner at the Milligan Vintage Trial.
The Swedish native oversaw Toyota's entry into F1 in 2002 and retired in 2003 as team principal. He remained a consultant until 2007.
Toyota also successfully competed in rally competition under Andersson's guidance, and he was key to the startup of Toyota Team Europe, which was spawned from his Andersson Motorsport team.
On his watch, the team won four drivers' and three manufacturers' championships. It also took second place at the Le Mans 24 Hours in 1999.
Andersson began his career at Toyota in 1969 as an engine-development engineer.
He was also an accomplished driver and got his first win at the 1967 Spanish Rally. His best season was in 1971, when he piloted a rear-engine Renault Alpine A110 to several victories, including the Monte Carlo, San Remo and Austrian Alpine rallies.
"Everyone at Toyota is extremely shocked and truly saddened at this terrible news," said Tadashi Yamashina, chairman of Toyota Motorsport, in a statement.
"Ove was an inspiration to our team and to many in motorsport. His passion for motorsport was legendary, and he is a great loss to our sport."
