JDelekto: First copy all of the folders and the contents of the games to their new location.
When you launch the GOG Galaxy client, log in and in the upper left corner, click on the GOG logo to open the menu and choose "Scan and import Folders".
The message you get should read: "GOG Galaxy will scan and import existing games. Installations from older game downloads may not be detected, but can be added manually (select game in Library and click More)."
Heed the warning about overwriting files in detected game folders.
If you choose the manual route, navigate to the game in your library (and it may show the blue INSTALL button). From there, click "MORE", select "Manage installation" and then "Import folder". This will take you to the same dialog, but from there you can import the individual game from your known install.
Thanks JDelekto and Randalator! I didn't even notice the drop down menu on that GOG logo! It worked perfectly!