Current England manager Gareth Southgate, who played under Venables at Euro 96, said: "Any player will have great affinity with the manager that gave them their opportunity, but it was quickly evident playing for Terry Venables that he was an outstanding coach and manager.
"Tactically excellent, he had a wonderful manner, capable of handling everyone from the youngest player to the biggest star.
"He was open minded, forward thinking, enjoyed life to the full and created a brilliant environment with England that allowed his players to flourish and have one of the most memorable tournaments in England history.
"A brilliant man, who made people feel special, I’m very sad to hear of his passing and my thoughts are with Yvette and all of his family."
Tottenham held a minute's applause before their match against Aston Villa on Sunday, and their players wore black armbands.
The FA said they were all "deeply saddened by the passing of... a true football icon". They added Venables "captured the imagination of many and enhanced the global reputation of the English game".
Former England captain Alan Shearer said: "Extremely sad news. The great Terry Venables has passed away. RIP Boss. I owe you so much. You were amazing."
Gary Linekar, the former England captain who played under Venables at Barcelona, added: "(I'm) devastated to hear that Terry Venables has died. The best, most innovative coach that I had the privilege and pleasure of playing for.
"He was much more, though, than just a great manager. He was vibrant, he was charming, he was witty, he was a friend. He’ll be hugely missed. Sending love and condolences to Yvette and the family. RIP Terry."
Ex-England defender Gary Neville, who won his first international call-up under Venables, told Sky Sports his former manager was "a joy to play for".
