He was an aggressive batsman and useful seam bowler who played 62 Tests for England and was captain between 1961-1964.
He led Sussex to victory in the first two editions of the limited-overs Gillette Cup and went on to make a surprise two-Test comeback in 1968.
In June 2021, he was inducted into the ICC Cricket Hall of Fame as one of the special inductees to mark the inaugural edition of the ICC World Test Championship final
A statement from Marylebone Cricket Club (MCC) described the club's much-loved former president as 'one of England's greatest ever cricketers'.
The statement read: "After a recent illness he passed away peacefully in the Compton Hospice in Wolverhampton at midday yesterday, surrounded by his family.
"Ted was a cherished husband, father and grandfather and one of England’s greatest ever cricketers.
"He was captain in 30 of his 62 Test matches and played the game with the same sense of adventure and fun that captures much of the story of his remarkable life.
"His off-field contribution to the game was substantial too, most notably his work, with Colin Cowdrey, on the Spirit of Cricket.
"Through his own PR Agency, he became a pioneer in cricket’s digital technology revolution and he was inducted into the ICC Cricket Hall of Fame earlier this summer.
"We kindly request that the privacy of Susan, his wife, and Genevieve and Tom, his daughter and son, is respected at this difficult time."
Speaking on Sky Sports, ex-England captain Michael Atherton said: "It's a very sad day for English cricket. He was a great icon of the English game.
"He was a great post-war batsman. He was a batsman of real dash and flair."
Dexter scored 4,502 runs at an average of 47.89 for England and took 66 wickets at 34.9. Six of his nine Test centuries were bigger than 140.
After retiring, he helped devise a ranking system for Test players and was chairman of selectors for England.
The ranking system was adopted by the ICC and formed the basis of today's system.
However, he had a difficult time as selector after inheriting a weakened England team between 1989 and 1993.
He was later named president of the MCC and was awarded a CBE in 2001.