Martin-Jenkins, affectionately known as 'CMJ' or 'The Major', joined the BBC in 1970 and succeeded Brian Johnston as the corporation's cricket correspondent in 1973.
He held the position until 1991, with a break between 1981 and 1984, and became a key part of the BBC's much-loved Test Match Special team.
Alongside working at the BBC, he was also cricket correspondent at The Daily Telegraph from 1991 to 1999, and The Times from 1999 to 2008.
In 2007, he became the only career journalist to give the annual Marylebone Cricket Club Spirit of Cricket Cowdrey Lecture, joining the likes of Richie Benaud, Imran Khan and Desmond Tutu.
He was awarded an MBE in 2009, and served as president of the Marylebone Cricket Club (MCC), owner of the Lord's cricket ground, in 2010.
Martin-Jenkins was diagnosed with cancer in January 2012, shortly after returning from commentating in the United Arab Emirates.
Jonathan Agnew, his successor as BBC cricket correspondent, led the tributes to him.
"CMJ, as he was widely known, was one of cricket's most respected writers and broadcasters," said Agnew in a statement.
"With modern media now preferring the views and experiences of former Test match cricketers, Christopher's authority and respect was not gained from a high-profile playing career, but a deep-rooted love of the game linked to a strong protective instinct which helped him earn the most coveted position of president of the MCC.
"Listeners to Test Match Special were all too familiar with CMJ's eccentricities - like going to the wrong ground for the start of a Test match. His legendary, chaotic time-keeping was very much part of his charm.
"Considering the years he worked as editor of The Cricketer magazine, and as correspondent for the BBC twice, The Daily Telegraph and The Times, and 40 years commentating on Test Match Special and the many books he wrote, it is doubtful that anyone has contributed more in a lifetime to the overall coverage of cricket than Christopher Martin-Jenkins."
Former England captain Sir Ian Botham, who was not known for his appreciation of journalists, described Martin-Jenkins as "a true gentleman".
He tweeted: "Very sad to hear of the death of the 'Major', Christopher Martin-Jenkins. Our thoughts are with the family. A true Gentleman."
Mike Griffith, the current president of MCC, said that Martin-Jenkins will be "sorely missed".
"I was fortunate to know him from his schooldays at Marlborough College and we became good friends," he said.
"Christopher gave tremendous service to cricket and to MCC, where he was president as recently as 2010. As a commentator and journalist he was passionate about upholding the values of the game and always expressed his views with clarity and humour.
"Everyone at MCC shares the sadness now being felt by the cricketing world that his live commentaries will never be heard again."
A statement from his family said: "Christopher died peacefully at home this morning after his brave resistance to cancer.
"The family is extremely proud of all that he did to pass on his love of cricket worldwide with his gift of communicating through the spoken and written word. He was above all a much loved husband, brother, father and grandfather."