Venables managed England from 1994 to 1996, most notably leading them to the semi-finals of Euro 96 on home soil.
He also had spells in charge of Barcelona, Tottenham and Australia.
"We are totally devastated by the loss of a wonderful husband and father who passed away peacefully yesterday after a long illness," read a family statement.
"We would ask that privacy be given at this incredibly sad time to allow us to mourn the loss of this lovely man who we were so lucky to have had in our lives."
The League Managers Association said: "The LMA is deeply saddened to hear of the passing of LMA member and former LMA president Terry Venables.