Cozier covered almost every West Indies series since 1962, and is one of the most respected cricket writer, broadcaster and historian to have come out of the Caribbean.
He had been hospitalised on May 3 for tests related to infections in the neck and legs.
Cozier, whose father Jimmy was also a cricket writer, began his commentary career with the Australia tour of the West Indies in 1965.
"Deeply saddened to hear of the passing of Tony Cozier today," the ICC posted on Twitter. "One of the truly great voices of cricket. A huge loss for the cricket community," the world body added.
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Commenting on the sad news, Damien O'Donohoe, Chief Executive Officer of the Caribbean Premier League said: "It was with great sadness that we learned of Tony's sad passing.
"To many fans across the Caribbean and beyond he was quite simply the voice of West Indies cricket. His love of cricket was a positive influence in telling the story across a golden era for West Indies cricket and he was hugely respected and loved, in equal measure, by fans of the game.