Venables guided England to the semi-finals of the 1996 European Championship on home soil before losing to Germany on penalties.
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.
"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.
The midfielder, who began his career at Chelsea, made two international appearances for England. He also played for Tottenham, winning the FA Cup as a player in 1967, as well as Queens Park Rangers and Crystal Palace.
"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.
