BrianKauth:
The process Eric Root describes is called "Adoption".
I had to do that a few months ago with my new Mac mini.
I don't remember exactly where, within the App Store, I saw it, but, first, I had to "force" the App Store to let me login (the Store menu -> View My Account).
I don't recall whether it was under my account, or if I went under Update, but I was given a message to the effect that three application needed to be adopted, before they could be updated.
It's even possible that I had to visit the application pages, where the "Get" button was shown as "Adopt", or some such.
Please get back with us if you continue to have trouble finding out how to Adopt those apps.