This is looking great so far!

We should expand this top comment to describe the format used to reference the review requdest ids in the commit message.
Speaking of which, maybe we should have the regex as a global up here so it can be customized easily.

I wonder if we could pull this information from the repositories ".reviewboardrc" file?
I don't think you should really spend a lot of time investigating this, or if it's even useful, just a thought.

Take a look into rbtools.utils.process, we include an execute command which has some extra helpers, including allowing you to specify the command as a list.

You should try to cut the summary down to one line. You could probably add the information about revserse order after a blank line.

Style: These doc strings should generally be a single line summary, with a blank line, and then additional information.
So, in this case:
"""Returns the review request ID referenced in the commit message.
We assume there is only one review request to be closed per commit. If

   an ID cannot be found we return None.

   """

I'd prefer if we explicitly return None rather than having it happen due to no call to return.
Maybe go with something like this?
review_request_id = (match and match.group(1)) or None
return review_request_id

This would probably look cleaner formatted as a list on multiple lines. See my previous comment about using rbtools' execute function.

This looks really good! Just some small nits here on a quick pass.

Nit: "each commit's commit message" is duped here.

I think we generally put the imports before any const declarations.

This looks

The "Reviewed at /r/" is really "Reviewed at <URL>/r/", right?

Maybe mention that this can be customized if a different format is required.
Given that, the regex should used named groups for the results, instead of positional groups. You can do that with:
r'.... (?<id>\d+)'

And then later:
m.group('id')

Should have a 'r' prefix, like:
REGEX = r'(....)'

No blanke line here.

No need for parens on the join string.

The parameters should align.
For logging calls, you don't need to use %. You can just pass the parameters as parameters to the function.

No blank line here.

No blank line here either.
You can just collapse these into one conditional.

Same comment about parens.

Same comment about arguments.

Two blank lines between top-level functions/classes/etc.

This is really "Reviewed at <URL>/r/"

Same comments about the regex.

No blank line.

Does this show the branch names, or just the SHAs?

No need for parens.

Oh, one more thing. I think this code would be better living in the RBTools tree. More accessible than pulling down the RB tree. It'll also help tie the hooks to RBTools versions more.
I didn't see any change yet for the RBTools modifications for the new the modules you made.

What do users see if they try to push but their push is denied because the review request isn't approved?

There's an extra blank line here. I think maybe we miscommunicated when you asked if files should end in a newline. Some editors don't add a \n at the very end of the file, but most do. It looks here like your files end in \n\n instead of just \n.

Extra blank line.

This looks good to me. Are there any other changes you want to make before I push it?