The Irishman, who owned a team in the sport between 1991 and 2005, had been suffering with an "aggressive" bladder and prostate cancer and passed away early on Thursday morning.
A family statement read: "It is with profound sadness that we announce the passing of Eddie Jordan OBE, the ex-Formula 1 team owner, TV pundit and entrepreneur.
"He passed away peacefully with family by his side in Cape Town in the early hours of 20 March 2025.
"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."
Jordan's team in F1 was named after himself and entered 250 races, winning four times during a 15-year spell.
He famously gave Michael Schumacher his debut during his first campaign and worked with the likes of Damon Hill, Martin Brundle and Jean Alesi.
Jordan later turned his hand to broadcasting and became a television pundit first for the BBC and then Channel 4, becoming known for his bold and brash style of analysis.
F1 president Stefano Domenicali paid tribute to Jordan, hailing him as a "protagonist" for the sport.
"We are deeply saddened to hear about the sudden loss of Eddie Jordan," Domenicali said.
"With his inexhaustible energy he always knew how to make people smile, remaining genuine and brilliant at all times.
"Eddie has been a protagonist of an era of F1 and he will be deeply missed.
"In this moment of sorrow, my thoughts and those of the entire Formula 1 family are with his family and loved ones."