The club are closely affiliated with the Royal Family with a picture of the Queen taking pride of place in the club’s home dressing room.
A club statement read: “The Directors, management, players and staff of Rangers Football Club are deeply saddened to learn of the passing of Her Majesty The Queen.
“Her Majesty served the people of Great Britain and the Commonwealth for over 70 years with incredible devotion and dignity. She will be gravely missed by not just our nation, but nations across the world.
“It is with great pride that her portrait has hung in our home dressing room at Ibrox Stadium as a mark of the club’s appreciation for her phenomenal service.
“The thoughts of everyone at Rangers Football Club are today with the Royal Family and all those mourning the loss of Her Majesty at this exceptionally difficult time.”
Hearts also paid tribute by holding a minute’s silence at the start of the second half of their Europa Conference League clash with Instanbul Basaksehir after the news broke during the half-time interval.
A statement read: “The club is aware of the sad passing of Her Majesty Queen Elizabeth II.
“As a mark of respect, we will observe a minute’s silence at the start of the second half of tonight’s Europa Conference League match and both teams and the officials will wear black armbands.”
Scottish football fixtures are now expected to be cancelled this weekend as the nation goes into a state of mourning.
Rangers are due to travel to Aberdeen on Saturday with Celtic hosting Livingston the same day.