If you sign in with your iTunes password and you use iTunes match, all your music will be on your new computer when you sign in.
If not, the best method is to use the new library on the new computer, and drag the folders/files from your external drive into the iTunes window. If you have space, I'd keep the iTunes location on your computer while doing this process to make it faster, then transfer it over to an external drive after the iTunes library is built.
You can point iTunes to the old library location on the external drive, but I've found that trying to transfer a library from one system to another is problematic. It's best to start fresh.