The Association of Irish Celtic Supporters Clubs also said Mr McNeill had "dedicated his life to Celtic".
The 33-year-old was adamant that "there will only be one greatest-ever Celtic captain and that is Billy McNeill".
A message from City read: "We are sad to learn of the passing of Billy McNeill who managed the Club between 1983-86". He would do anything to help you.
In two spells as Celtic manager, he won four titles and four cups, including a league and cup double in the club's centenary season, 1987/88.
Manager Neil Lennon said: "I love Billy's statue, which is the first thing you see whenever you walk up the Celtic Way".
Tributes have been paid to the man Celtic fans called Cesar.
Another ex-Celtic player, Davie Provan told Sky Sports News: "He was a terrific man-manager, really fair with the players".
"Billy set the benchmark as a Celtic player and captain, and that's something everyone who pulls on the jersey has to aspire to", Brown said.
Tributes came in from the likes of Rangers and Inter Milan, the latter remembering a "great opponent" from the 1967 European Cup final. He made 790 competitive appearances for Celtic - more than any other player in our history - and during that time he won nine league titles, seven Scottish Cups, six League Cups and, of course, the European Cup triumph in 1967.
Chief executive Peter Lawwell said "there was no more fitting candidate" for the honour. The Celtic Legend was present when Kieran signed his first Celtic contract.
Billy McNeill made such a towering contribution to Scottish football that when it comes to an appreciation of his life it is hard to know quite where to start, so a personally-assembled mountain of silverware seems as good a place as any.
McNeill is in the Scottish Football Hall of Fame, and was voted Celtic's greatest ever captain in 2002. He was also a truly good man and will be a loss to everyone who knew him.
McNeill won most of his relatively modest total of 29 caps for Scotland early in his career, after making his debut in the infamous 9-3 defeat by England in 1961.
McNeill had suffered from dementia for a number of years and a statement issued by his children said: "It is with great sadness that we announce the death of our father Billy McNeill".