Venables guided England to the semi-finals of the 1996 European Championship on home soil before losing to Germany on penalties.
"We are totally devastated by the loss of a wonderful husband and father who passed away peacefully yesterday after a long illness," the family said in a statement.
In addition to his spell in charge of Tottenham, during which he won the FA Cup in the 1990-91 season, he also took charge of Crystal Palace, Leeds United and Barcelona in a glittering managerial career.
During his time at Barcelona, Venables earned the nickname El Tel, winning LaLiga and reaching the European Cup final in 1986. Venables was also responsible for bringing British strikers Gary Lineker and Mark Hughes to the Nou Camp.
"The best, most innovative coach that I had the privilege and pleasure of playing for," Lineker, who also played under Venables at Spurs and England, wrote on X, formerly known as Twitter.
"He was much more, though, than just a great manager, he was vibrant, he was charming, he was witty, he was a friend."
Venables started his professional career as a player with Chelsea in 1960 and played for Tottenham Hotspur, Queens Park Rangers and Crystal Palace before retiring to take over the manager's role there.
As a player, he made over 500 league appearances and won the League Cup with Chelsea in 1965 and the FA Cup with Spurs in 1967. He made two international appearances for England.
Venables also had a two-year stint as chief executive of Spurs from 1991-93.
"We are extremely saddened to learn of the passing of Terry Venables, our former player, manager and chief executive, who passed away on Saturday," Spurs said in a statement.
