The left-handed opener played 77 Tests, scoring 5,138 runs at an average of 43.54.
Edrich, who was diagnosed with leukaemia in 2000, scored 103 first-class centuries and was awarded an MBE in 1977.
Sir Ian Botham wrote on Twitter: “Very sad news today to wake up on Christmas Day and to be told that John Edrich has passed away !!
“A wonderful man who I was lucky enough to spend some quality time with…RIP”
ECB CEO Tom Harrison said: “With John’s passing, we’ve lost a prolific and fearless batsman – one of the select few who have scored more than 5,000 runs for England.
“His duels with some of the world’s best fast bowlers were legendary, and it’s a testament to his ability that his 310 not out against New Zealand in 1965 remains the fifth highest Test score by an English batsman.
“He will be sadly missed, and our thoughts are with his family and friends.”