Neil described Burnet as "one of the greatest journalists of his generation", adding: "He will also always be recalled by family, friends and colleagues for his unparalleled professionalism, humour and gentlemanly kindness, especially to journalists starting out on their careers.
"Joy it was to be in his company and he was an inspiration to many who followed in his footsteps - the broadcasters' broadcaster."
Meanwhile, a statement on behalf of Burnet's family has been released to ITV News. It says: "He passed away peacefully in the middle of the night at the Beatrice Place Nursing Home in Kensington, where he was being cared for after suffering several strokes."
Burnet joined ITN in 1963 as the company's political editor, then four years later he became a news anchor, the role for which he is best known.
John Hardie, chief executive of ITN, said in tribute: "ITN stands on the shoulders of giants, none greater than Sir Alastair Burnet. He defined newscasting for a generation and his influence is still clearly evident today.
"He set the bar to a standard that has never been surpassed, and perhaps not even equalled. Sir Alastair will be sorely missed by many here at ITN, but his legacy lives on."
Early in his career, the broadcaster hosted ITV's coverage of the iconic Apollo 11 moon landing in 1969.
In 1974 he defected to the BBC, where he worked on Panorama and fronted two general election broadcasts, before rejoining ITN in 1976.
Burnet, also a respected print journalist, edited The Economist in the 1960s and the Daily Express for a brief period between 1974 and 1976.
Burnet, then 63, read his last bulletin on News at Ten in August 1991.