The initiative will return popular stock issues to the service so that they can be recirculated for more readers to enjoy.
Greenwich Libraries Partership Manager Paul Drumm said: "Greenwich is a borough of avid readers - our library service is one of the most popular in the country - issuing up to 1,360,000 items each year.
"Its success depends on our book stock being freely circulated so the maximum number of library members have the opportunity to read them.
"Our amnesty invites those who have unreturned books to 'start a new chapter' and bring them back in - without the fear of fines.
"So take a look under your bed and behind the sofa for those items that are hiding from view.
"Bringing back your overdue books is also a great way to reconnect with library services and see what's new."
From now until May 31, 2025, Greenwich library users can 'wipe the slate clean' and start afresh by bringing back any overdue books or materials to any Greenwich Library branch. All outstanding fines related to those items will be waived.
Members who have lost their library card, will be provided an environmentally-friendly biodegradable replacement free of charge - or they can download a digital library card on their phone via the Greenwich Libraries App.
After the amnesty period ends on May 31, 2025, overdue charges will once again pertain where applicable.
Library members are encouraged to take advantage of this limited-time opportunity to return items stress-free.
For more information about the amnesty program and other library services, please visit https://www.better.org.uk/library/london/greenwich or stop by your nearest Greenwich Library branch.