I have had the same issue lately. And this is a great chance to record and share your notes. :)
I assume that you are using Xcode and Organizer (do not download the application)
Step 1: check Keychain Access.app.
You should have two certificates (which you download from the mac dev center). Each of them must be associated with a private key. In the picture, I have only one certificate "nacho4 ..." associated with the private key "nac ...". So I have to go to the mac dev center and upload my certificates in order to continue. Download them and drag them into the "login".

Step 2. Make sure you can create the application with the correct configuration.
In my case, I am setting up three configurations. Debugging: can be debugged + without a signature (for development) Release: cannot be debugged + no signature (mainly for internal beta versions, etc.) Distribution: cannot be debugged + signature (for distribution of the app store)
Go to "Assembly Information"> "Sign Assembly"> Make sure you sign the code with the correct icon. Something like: "A third-party application for Mac developers. My company Inc." * If you do not see this, then something is wrong with your certificates in Keychain Access.app. Verify that your certificate is associated with the private key 
Step 3 Make sure you have built the correct configuration.
(Yes, it’s obvious, but this was the last time it happened to me. It is for this reason that you may receive an “Invalid Signature”). In the "Edit Schema" panel, make sure that you have the correct configuration in the "Archive" section. In my case, this is "Distribution" (by default, "Release")

Please note that if you do not do this correctly, you can send your binary to Apple, but after a few minutes you will receive an “Invalid Signature”. Since the certificates are fine, but the application is not signed.
Step 4: Build the app and submit it
Xcode> Product> Archive 
The organizer will appear. Now just send it.
I found that checking the archive is useless, because sometimes even the verification fails, I can send my application without errors. I read this from other threads, so not only me. Therefore, if you are sure that this is the version you want to send to Apple. just click the submit button.
You are asked for your username and password. Then you get another menu to select the application (it has only one option, at least in my case), and then select the signature identifier that I think. It is important! Make sure a third-party Mac Developer Installer is selected and everything should work.

If you don’t see the option "Third-party Mac Developer Installer" in the last menu, then something is missing in your keychain. (Installer certificate from mac dev center)
Please note: if you don’t do it right, you can send your binary, but after a few minutes you will receive an “Invalid Signature” message from iTunes Connect, because the application may probably be well signed, but Apple certificates will be incorrect.
Hope this helps.