The club submitted plans to Glasgow City Council for the tribute which will mark the greatest achievement in their history.
Drawings submitted to the planning department show images of McNeill lifting the trophy above his head as Celtic became the first British club to win the competition in Lisbon in 1967.
Celtic announced plans for the bronze statue, which will be positioned on Celtic Way outside the stadium, in April.
No objections to their planning application were received and it has now been approved by the council, allowing construction to begin.
In a written report, council planners said: “The proposed structure will be located well away from the nearest footpath. Consequently, it will not obstruct the footway or interfere with pedestrian flows.
“The proposed sculpture is not over-dominant in terms of its scale and form. The statue will be durable and robust.
“The proposal is considered to comply with the relevant Development Plan policy and design guidance.”
McNeill, known as Cesar, won nine league championship titles in a row, seven Scottish Cups and six League Cups during a glittering Hoops career.
His lifelong-association with the club also included two spells as manager during which he led the team to four league titles, three Scottish Cups and a League Cup.
He will become the fourth Celtic icon to be honoured with a statue after founder Brother Walfrid, celebrated manager Jock Stein and revered winger Jimmy Johnstone.
Speaking earlier this year, the 75-year-old said: “When I was contacted regarding the statue I was completely taken by surprise.
“Whenever I walk up the Celtic Way, I look on with a great sense of pride at the sight of Brother Walfrid, Big Jock and my old team-mate and friend Jinky rightly taking their place almost as guardians of Celtic Park.
“Every time I look back at this special club’s history and what we achieved it fills me with joy, and now to be told I am to be honoured beside these Celtic greats, this really is a special day for me and all my family.”
The statue will be sculpted by John McKenna, who was also responsible for the tribute to Stein.
Celtic chief executive Peter Lawwell said: “Growing up in the 1960s and 1970s as a Celtic supporter, Billy McNeill was an inspiration to me and someone of huge stature in the game, not only on the field but also off it, as a statesman, a leader and a figurehead for our great club.
“His achievements for Celtic are simply outstanding and across a period of 27 years he gave so much to the club.
“We are delighted already to have Billy as our Ambassador at the club but the Board felt unanimously that he should recognised in this way, given all that he has contributed to Celtic over so many years.
“We look forward to the unveiling of the statue, which we are sure will be a great tribute to a great man.”