The "Robben Island Bible" - which is actually a copy of the complete works of Shakespeare - belongs to man who was in jail at the same time as the former South African president.
It went on display at the city's Mitchell Library yesterday as the world marked Nelson Mandela International Day.
The book will be on show there for three months.
Robben Island prisoner Sonny Venkatrathnam passed the book to 33 of his fellow inmates, asking them to sign a passage that meant something to them.
Mr Mandela underlined a passage from Julius Caesar and signed his name beside it on December 16, 1977.
The passage he highlighted reads: "Cowards die many times before their deaths. The valiant never taste of death but once.
"Of all the wonders that I have heard, it seems to me the most strange that men should fear, seeing that death, a necessary end, will come when it will come."
Events were being held all over the world yesterday to mark Mandela's birthday. The former South African president died on December 5 last year at the age of 95.
The commemorations in Glasgow included a ribbon-tying ceremony and time for reflection outside St George's Tron Church in Nelson Mandela Place at 1.30pm.
Special guests at the ribbon-tying ceremony, organised by Action for Southern Africa (ACTSA) Scotland, included Mandela's granddaughter Tukwini Mandela.
Athletes from Team South Africa here for the Commonwealth Games also attended.
Glasgow was the first city in the world to award Nelson Mandela the Freedom of the City in 1981 when he was still a prisoner in Robben Island.
Five years later the city again honoured the anti-apartheid campaigner, renaming St George's Place after him.
After he was released from jail, Mr Mandela visited Glasgow in 1993 to thank the city for its support.