Antic died at a clinic in Madrid late on Monday after battling pancreatitis in his latter years.
The former Serbia manager is only the second person to manage both Real Madrid and Barcelona after Enrique Fernandez Viola.
The highlight of Antic’s managerial career however came at Atletico Madrid, where he had three spells, leading the Rojiblancos to a famous league and Copa del Rey double in the 1995/1996 season.
"Today is a sad day for all Atletico fans and for the football world," Atletico Madrid president Enrique Cerezo said in a statement.
"A great person leaves us and one of the architects of Atletico Madrid's golden age. We'll always remember the Liga and Copa del Rey trophies that we won under his command. I'm proud to have known him."
"With the loss of Radomir, a piece of the heart of the club leaves us," the club's chief executive Miguel Angel Gil added.
"With him I personally learnt to win, I learnt to live with passion the little things that make you a better man and a better professional."
Real Madrid captain Sergio Ramos tweeted: "You made Atleti bigger, you made our rivalry bigger. Goodbye to a unique career: Atletico, Barca and Real Madrid among others. RIP."
Antic counts the likes of Real Zaragoza, Real Oviedo, Celta Vigo and Chinese Super League side Hebei China Fortune among his former clubs.
