It was opened on Monday by SDLP councillor and Mayor of Derry City and Strabane District Council, Brian Tierney.
Signing the book, SDLP leader Colum Eastwood said the island had lost its most significant political figure of the 20th Century.
Mr Eastwood compared his predecessor to the famous US civil rights leader Martin Luther King.
“John Hume was our Martin Luther King,” said the Foyle MP.
“He was the greatest Irishman ever.
“He achieved something that no-one could ever achieve before him.
“He ended the Anglo-Irish conflict, the conflict that had gone on for 800 years.
“And he gave my generation the opportunity to achieve our political goals peacefully and democratically, and that is an enormous legacy.”
The neighbouring district of Fermanagh and Omagh Council has also opened an online book of condolence on its website.
The former Foyle MP and MEP had dementia and in recent years had lived in a care home in Derry.
Mr Hume died in the early hours of Monday morning at Owen More care home on the Culmore Road. He was aged 83.