You must clearly state the following on your site:
[Insert your name] is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to [insert the applicable site name].
While we have this disclosure already built-in inside the widgets, our recommendation is to have the disclosure, additionally, on every page. We like to be safe. You can easily do this by creating a new text widget in your sidebar or footer. Having said that, it may suffice not not include the widget since it is already available inside the widget as a footnote link.
The widgets also include additional disclaimers, as required by Amazon Associates Operating Agreement, indicating the last product update time.