Messages of condolence from around the world continue to pour in for McNeill - who became the first British man to lift the European Cup when the Hoops beat Inter Milan in 1967 - following his death on Monday aged 79.
And former Gers defender Greig paid his own respects as he led a delegation from Ibrox across the city.
Joined by the Light Blues’ managing director Stewart Robertson and board member Andrew Dickson, Greig placed a wreath of red, white and blue flowers under McNeill’s statue along with a card that read: “Always remembered, from the directors, players and staff of Rangers Football Club.”
The touching gesture was met with applause from the crowd of Celtic supporters who had gathered to remember the man known affectionately as “Cesar”.
Greig was leading out the Light Blues during the same period in the late 1960s and early 1970s when McNeill was Celtic skipper.
But as well as being derby opponents, they were also team-mates for Scotland and grew to be close friends.
Greig, now Rangers’ honorary life president, told the Celtic website: “Billy was always an out-and-out gentleman.
“He always treated me with the greatest respect and we enjoyed a lot of times helping charities and different things off the field. He was a good, good friend and I was very sad to hear of him passing away.
“He was a giant on the park. He was actually too good-looking to be a centre-half.
“Apart from being a great defender, Billy also scored so many goals because he was so great in the air
“That was one of the things we always had to watch when we played against Celtic, although there were plenty of other problems for us in that team. It was a great Celtic side.”
Meanwhile, Rangers nine-in-a-row captain Richard Gough has also added his tributes to the Celtic great.
McNeill was part of Jock Stein’s side who first achieved the feat as they won every title between 1966 and 1974 but that did not stop him calling up Gough to congratulate him on equalling the Hoops’ record run in 1997.
Posting on Facebook, he said: “My condolences go out to Billy McNeill’s family.
“He was a true great of Scottish football and a wonderful person. One of the first people to phone me up and congratulate me on leading Rangers to nine championships.
“That says it all about the respect the man had. We have lost an icon today. RIP Big Man.”