Keating passed away at St Michael's Hospice, Hereford, on Friday (January 25) after suffering from pneumonia.
He originally joined The Guardian in 1963 as a sub-editor but left a year later to work in television for six years, including latterly as news editor at Thames TV.
Keating rejoined The Guardian in 1970, and wrote for the paper and its sister title, the Observer, until last December.
He won many friends and fans for his writing and lively personality, and there have been many tributes paid to him online.
The Guardian's sports editor Ian Prior tweeted: "Immeasurably sad to announce the death of Frank Keating, one of the finest of all Guardian sport writers."
On his Twitter page, Piers Morgan posted: "RIP Frank Keating - truly one of the greatest sportswriters ever."
The Daily Telegraph's chief sports reporter Paul Kelso added: "Very sad to hear of Frank Keating's passing. I won't be the only one inspired into newspapers by his brilliance. RIP."
BBC chief cricket correspondent Jonathan Agnew tweeted: "So sad to hear Frank Keating has died. Lovely gentle man, great company and a wonderful writer."
Alan Rusbridger, the editor-in-chief of The Guardian and Observer, said that Keating had been an "immense figure in sports journalism for more than 50 years".
"He was a unique character, combining sophisticated sporting knowledge with a deep empathy and understanding of the human side of sport," said Rusbridger in a statement.
"Frank was also universally popular with an inspiring and uplifting personality that was infectious."
He added: "As a writer, Frank deserves to be placed in the very elite of British sportswriting in the last century - and amazingly, though ill, was still writing his wonderful weekly column in the Observer up until a few weeks ago.
"Our thoughts and condolences are with his family at this sad time."