The head coach described Jardine as "a Rangers legend in every sense of the word" and a "truly remarkable human being".
He said: "There have been many great names associated with Rangers Football Club in our 142-year history and Sandy is a Rangers legend in every sense of the word.
"We are all devastated by the news he has passed away, we have lost a great man today.
"I had the privilege of watching Sandy playing for Rangers when I was a young boy, I had enjoyed the pleasure of working with him closely since I returned to the club in 2007 and he was a truly remarkable human being."
McCoist went on to say that Jardine, who died following an 18-month battle with cancer, will go down as one as the greatest Rangers players of all time, and offered condolences to his family.
"His achievements both on and off the pitch are second to none and I was honoured to regard him as a friend. He gave everything for this great club and worked tirelessly in a number of roles because he wanted to ensure the traditions, history and standards at Rangers were maintained," he added.
"He was respected not only by Rangers fans but also the wider football community and he is a huge loss to the game. We will never see his like again in the modern era.
"He recently told me he was proud to be a Ranger and wanted to be remembered forever as a Ranger. Well Sandy you will go down in history as one of the greatest of all time and we will miss you terribly.
"It is a very sad day for everyone associated with Rangers and our thoughts are with his wife Shona, his children Steven and Nicola, his grandchildren and the rest of his family and friends."
Jardine made more than 800 appearances for Rangers during his playing career and scored 77 goals.