Yes because the games are tied to your Steam account, not your computer.
All that will happen is Steam will detect you are trying to login from a different computer, and will send a verification code to your e-mail address that you'll need to enter in Steam.
You'll need to reinstall them obviously, as well as transfer your saved games if they're not in the cloud. (Skyrim supports Steam Cloud)
So basically you can use your Steam account from any computer, but you can only have one session going on at a time.