The ex-Scotland international, capped 38 times by the national team, passed away after an 18-month battle with cancer.
Jardine spent five decades at Ibrox Stadium, in both a playing and non-playing capacity, and turned out for Scotland at two World Cups.
"Sandy Jardine epitomised everything that is good about Rangers Football Club. He was a man of principle and class and his contribution during his career both on and off the pitch was truly remarkable," said Rangers chief executive Graham Wallace in a statement.
"He was a credit to the Club for decades and in my meetings with him his dignity, class and love for Rangers shone through. On behalf of everyone at Rangers I wish to send my sincere condolences to Sandy's family and friends at this difficult time."
Jardine made more than 800 appearances for Rangers during his playing career and scored 77 goals.