The Irishman revealed in December that he was suffering with bladder and prostate cancer, which had spread to his spine and pelvis.
“It is with profound sadness that we announce the passing of Eddie Jordan OBE, the ex-Formula 1 team owner, TV pundit and entrepreneur,” his family said in a statement.
“He passed away peacefully with family by his side in Cape Town in the early hours of Thursday at the age of 76, after battling with an aggressive form of prostate cancer for the past 12 months.
“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, which he named after himself, entered 250 races between 1991 and 2005.
They won four times, with Damon Hill leading home Jordan’s best-ever result – a one-two finish at the 1998 Belgian Grand Prix.
Jordan also handed Michael Schumacher his F1 debut at the 1991 Belgian Grand Prix, with the German going on to win a record-breaking seven world championships – an accomplishment only matched by Lewis Hamilton in 2020.
He sold his F1 team in 2005 and subsequently became a TV pundit for British television.
F1 chief executive Stefano Domenicali said ahead of this weekend’s Chinese Grand Prix in Shanghai: “We are deeply saddened to hear about the sudden loss of Eddie Jordan.
“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 One family are with his family and loved ones.”
Aston Martin F1 team principal Andy Cowell described Jordan as a “one-off”.
“His vision laid the foundations for us and he leaves a lasting legacy for the entire motorsport community,” he said.
“Today we pay tribute to a legend of the sport and our thoughts are with his family, friends, and colleagues.”
Former British driver Martin Brundle was among others who paid their tributes.
“RIP my friend. Condolences to each and every one of your lovely family. What a character. What a rock star. What a racer,” he said.
Williams’ Carlos Sainz said: “Very sad to hear the news Eddie Jordan passing away. He was a true friend of his friends and really charismatic person inside the F1 world.”
Presenter Jake Humphrey, who worked alongside Jordan at the BBC, tweeted: “Utterly devastated. EJ has left us. Formula One won’t see the likes of Eddie ever again where a guy with a love for racing can hustle his way into the sport and end up winning races.
“More important than race wins though, he won hearts. I will never forget how his face would always light up whenever he saw a Jordan GP jacket, flag or cap, as we travelled the world together years after the team had been sold.”