The App Store app uses spotlight to find all the apps on your Mac that were downloaded from the store. You simply need to delete all those apps from the Mac (your personal data and settings do not get deleted) and re-download the app.
Step one of course, it to sign out from the other account if you haven't done that yet. When the App Store App is running, choose the Store -> Sign Out menu item.
The details on how the App Store app actually knows if an app was downloaded is buried inside the application bundle as descrtibed on this quesiton about avoiding updates to apps entirely.