Members of the public can also sign online
The Mayor of Derry City Hilary McClintock has opened a book of condolence in memory of Martin McGuinness.
The former deputy First Minister passed away earlier at the age of 66.
The book is open for members of the public at the Guildhall from 12 noon.
Members of the public can also sign online via the council website.
Expressing her condolences, Mayor McClintock said: "As mayor I want to take this opportunity to express my sincere condolences upon hearing the news of the passing of Former Deputy First Minister Martin McGuinness.
"Martin McGuinness was a towering figure in Northern Ireland in general and in the city of Londonderry in particular.
"Whilst there will continue to be a diverse range of opinions on Mr McGuinness' contribution to society over his lifetime it is clear that he had a passion for the city and the wider North West area. In recent years his contribution helped build on the relative peace we now enjoy.
"As mayor of the city and surrounding district I know that many people are today both in shock and deeply saddened by his passing.
"I want to extend, both personally, and on behalf of the Council, my sympathy to Mr McGuinness' wife Bernie and his family circle at this deeply traumatic time."