Described as "one of England's greatest ever cricketers" and "a true gentleman", Dexter captained his country between 1961 and 1964 and went on to become chairman of selectors.
He spent his latter years in Wolverhampton, where he was a member of Wolverhampton Cricket Club and volunteered teaching children to read at the city’s Graiseley Primary School.
He was also a keen golfer and regularly played at South Staffordshire Golf Club.
A statement from the Marylebone Cricket Club (MCC) said Dexter passed away peacefully in the city's Compton Hospice at midday on August 25, surrounded by his family.
It adds: "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."
Known as a swashbuckling and elegant batsman, Milan-born Dexter, who played for and captained Sussex at county level, represented England in test matches between 1958 and 1968.
He became renowned for his powerful hitting, and is one of only five England batsmen to record a score of 50 in six consecutive innings.
Nicknamed 'Lord Ted' for his debonair manner, his most memorable innings include smashing 70 off 73 balls against the West Indies at Lord's in 1963, and an incredible six-hour, 180-run stand against Australia at Edgbaston in 1961.
He ended his Test career with 4,502 runs at an average of 47.89, and also took 66 wickets at an average of 34.93.
Following his retirement, Dexter went into journalism and broadcasting, before he returned to cricket in 1989 to serve terms as England’s chairman of selectors and president of the MCC among other roles.
A pioneer in cricket’s digital technology revolution, he also helped to create the Deloitte Rankings for test players, which went on to be adopted by the International Cricket Council (ICC). He was awarded a CBE in 2001.
In June this year, Dexter was inducted into the ICC Hall of Fame, choosing to receive his cap at Wolverhampton Cricket Club, where he became a member in 2017, rather than making the journey down to London.
Club chairman Mike Elphick said: "He was a great supporter of the club and only recently we had been discussing making him an honorary member.
"We'll certainly be looking at doing something in his memory. It was such an honour for us that he chose to have the ICC Hall of Fame presentation in Wolverhampton rather than down at Lord's.
"He felt at home here. He will be remembered as a true gentleman and will be greatly missed."
Dexter and his wife Susan moved to Tettenhall from the Cote D’Azur in France to be closer to his family, having previously been a regular visitor to Wolverhampton to babysit his grandchildren.
In an interview with the Express & Star last November, Dexter cited his sometimes difficult four years as the chairman of selectors as the proudest moment of his eventful career.
The period saw him bring in a raft of reforms which have long been accepted as laying the foundations of the England team’s renaissance after a period in the doldrums, including fixed term contracts for players and extending county games from three days to four.
Explaining his decision to move to Wolverhampton, he said: "We didn’t want to live in London, nor could we afford the property prices, so we felt we would be more use as grandparents in Wolverhampton."
England's players marked his passing today by wearing black armbands in the test match against India at Headingley.
Among those to pay tribute was former England cricket captain Michael Vaughan, who said: "Ted Dexter was someone who always went out of his way to offer so much great advice to me and many others.
"Seeing him arrive for lunch on his motorbike and then sit and listen to him discuss all cricketing issues was always a joy."
He is survived by his wife Susan, and his daughter and son, Genevieve and Tom.