Cozier passed away yesterday at the age of 75 following a long illness.
He 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.
"First of all we have to appreciate that this is a very, very sad day. Not just for West Indian cricket, but for Tony's entire family," said Michael Holding, whose autobiography 'Whispering Death' was co-authored by Cozier.
South African speedster Dale Steyn said, "What a sad day for cricket, especially WI cricket, and the fans. RIP Mr Cozier. Gone but you will never be forgotten."
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Darren Sammy, who led West Indies to their second T20 World triumph, said, "Condolences go out to the families and friends of #TonyCozier That voice will forever be in my head #RIPTonyCozier."
Once a teammate and captain of Steyn, Graeme Smith said, "I'm really upset about the passing of Tony Cozier. He was one of the finest the comm box has ever been blessed with and a good friend. RIP."
Cozier, whose father Jimmy was also a cricket writer, began his commentary career with the Australia tour of the West Indies in 1965.
Born in Bridgetown, Barbados in 1940, Cozier began a 50-year media career with his father Jimmy, who was managing editor of the St Lucia Voice and Barbados Daily.
Henry Blofeld, who has done commentary with Cozier, wrote on twitter, "How desperately sad. Tony Cozier was a brilliant commentator & a truly great man. West Indies cricket has lost a man it will never replace.
Cricket Australia also paid tribute to the veteran West Indian commentator.
CA Chief Executive James Sutherland said in a statement: "Like generations before me I had the great privilege of listening to Tony Cozier bring Caribbean cricket to millions of Australians. His mellow West Indian accent, astute observations and clever turn of phrase added to the colour and excitement of Caribbean tours to Australia.
"Tony was also a pioneer as a founding commentator of World Series Cricket, when the game lit up with day-night matches, changing cricket forever.