He ran his own Jordan team in the 1990s and 2000s in F1 and became a popular pundit on TV after selling the team in 2005.
Jordan had been undergoing treatment for what he had called “quite aggressive” cancer of the bladder and prostate, which spread to his spine and pelvis.
The family said in a statement Jordan “passed away peacefully with family by his side in Cape Town” early on Thursday.
“EJ brought an abundance of charisma, energy and Irish charm everywhere he went. We all have a huge hole missing without his presence. He will be missed by so many people, but he leaves us with tonnes of great memories to keep us smiling through our sorrow.”
Irish businessman Jordan operated his own racing team in lower-level series before moving up to F1 in 1991, giving future seven-time champion Michael Schumacher his first race that year.
Other drivers over the years included Damon Hill, who won the 1996 championship with Williams, future Ferrari driver Rubens Barrichello, and Heinz-Harald Frentzen, who was third in the championship for Jordan in 1999.
Jordan Grand Prix won four races before Jordan sold the team in 2005. Following more sales and name changes since then, the team competes as Aston Martin.
The 76-year-old Jordan also acted as the manager for car design great Adrian Newey when he left Red Bull for Aston Martin last year. (AP)
