Here is what I did to get all commits and tags signed by default and recognized as Verified by Github:

1. Create a new GPG key

   I already had one GPG key but with other email. Although it is possible to add another email to the key, I wanted to separate things, as I am going to use this key too many times for signing every commit, and also will add its passphrase to the gpg-agent. Those things may make the GPG key more easy to compromise.

   I have used gpg2 as is more suitable for destkop environments than gpg (but the commands are compatible).

   gpg2 --full-gen-key
   

   I created a 4096-bit RSA/RSA key that don't expire and with the name set to the same value of the git config user.name, and the email set to the git user.email. It is important that this values are equal and that you don't add any comment to the key to allow git to correctly get the suitable key automatically.

2. Add the key to Github

   Here I added the key that I exported with

    gpg2 --export <key-id>
   

   The <key-id> is the key id of the newly-created key. It is printed when the key ends generating. You can also get it with gpg2 --list-secret-keys.

3. Set git to sign by default

   As I am using gpg2, I have to tell git to use it too, as gpg won't be able to read GPG private keys generated with gpg2 (the opposite is also true, gpg2 won't see private keys generated with gpg, but both of them see the same public keys).

   git config --global gpg.program gpg2
   

   Now, to sign every commit by default:

   git config --global commit.gpgSign true
   

   If you use git-flow and you want your release and hotfix tags to be signed as well (taken from here)

   git config --global gitflow.release.branch.sign true
   git config --global gitflow.release.finish.sign true
   git config --global gitflow.hotfix.finish.sign true
   

4. Add the GPG key passphrase to the gpg-agent

   In Ubuntu, I only have to use the key once (gpg2 --sign --default-key <key-id>) and in the dialog that appears asking me the passphrase of the key it will also have a checkbox to add the passphrase to the keyring (ie. remember it). So, check it and you won't have to type the passphrase anymore while the gpg-agent is running (which is automatically started when you log-in on the X session).

5. [OPTIONAL] Tell git what key to use for signing

   If you followed my advice of naming the key with your git name and email, you don't have to do anything here, as for every sign operation, git will look for a key with the format user.name <user.email>, and it will match your newly created key unless you change them.

   I like having it that way, because if you use another user or email for a specific repo, git will try to search for a corresponding key for it and fail if it doesn't find any. So you will get notified instead of silently keeping signing commits with the same key for this repo too.

   If you still want to sign commits with the same key having a different user or email, you have two options: setting signinKey for that specific repo (as we will see later), or adding that user <email> identity to the GPG key.

   GPG keys can have multiple identities (ie. name-email combinations), and adding one will not modify the key id, meaning that you don't have to change the key in every site you have uploaded it to (like GitHub). Just add the new identity (with gpg2 --edit-key <key-id> and then typing adduid) and upload the new exported key to the relevant site (the site of the specific repo usually).

   If you didn't follow the advice or want to use a key with different name or email than your git name and email, or simply want to add a comment to the key identify and you don't want to have multiple identities as I have talked about before, you can tell git to always use the same key for every sign operation with the following command:

   git config --global user.signingKey key-id
   

   Remove the --global if you want to set it only for the current repository.

6. Commit as usual!

   All your new commits will be signed, and the tags you create with git tag -s too! Also, the git-flow created tags by git flow feature finish and the like will be signed too!.

   You can confirm in the GitHub web interface that it is working correctly by looking at the Verified tag of the commits.

   In git, you can use git log --show-signature to display the signature info, or git log --format=raw to view the raw signatures in armored format (so that you can input them to gpg2 for inspection). Use git tag -v tag-name to verify a signed tag.