Maybe I am wrong, but I am going to assume that you are asking for something different than the interpretation offered by all the reply posts that I have read here. The body of your post made it sound like you wanted all links from the HTML of each page (which is why you got the replies that you got), but the title of your post makes me think you only want to export the URL of each tab that is currently open (in one or more browser windows).
If it is true that you want to "export the URL corresponding to each open tab", then:
I found this Google Chrome Extension:
When it works, it is quite nice. However, I found it to be buggy. When I chose the option to export tab URLs from all
open windows, it failed every time. The design is bound to cause bugs because it doesn't allow you to save the text into a file; instead, it offers to send the text as an email message. If the size of the text is too large, that is bound to cause problems in various email protocols. Fortunately, however, you can select all the text and then copy it into the system buffer. You can then do whatever you want with it: save it to a file, email it, whatever.
It worked fine as long as the number of URLs that I wanted to aggregate was not too large.
I am thinking of writing a Google Chrome extension that will achieve what "Export Tabs" achieves, but I will add some features to it that I want, e.g. saving the results to a file. And hopefully I can figure out why the "email" option fails when the text size gets too large. Hopefully Google's HTTP API is rich enough to support sending a fairly large body of text.
If I succeed, I will try write an add-on for Firefox also.