Manging a secret gpg key-pair across two computers is relatively simple.

Export the secret keys

gpg --export-secret-key -a your_email@address.com > myprivate.key

Export your public keys

gpg --export -a your_email@address.com > mypublic.key

Import the keys

gpg --import mypublic.key
gpg --import --allow-secret-key-import myprivate.key

That’s all there is to it.