Signature images not sending in Outlook 2013 or Outlook 2016

I’ve created my HTML signature in an external application and then placed the files (including txt and rtf versions) in the Signatures folder. This signature contains a picture and looks correct when composing a new message or reply. However, when I send the message, the recipient does not see this picture.

I’ve successfully used this signature for years with Outlook 2010 and the issue only occurs when I send a message with this signature from Outlook 2016.

Why is this happening and how can I make my signature work with Outlook 2016?