I’ve been using Oracle’s VirtualBox for a few years now but postings on how to move the Virtual Disks around have tended to center around modifying the VirtualBox.xml file.
There is currently, and I think always was, a simpler way to accomplish this task. Here are the steps.
********** UPDATED for V4.3 (finally) **********
1. With the VM in the powered-off state, copy the VDI file from point A to point B.
2. Start VirtualBox and a Warning dialog may appear to tell you that the .vdi file disappeared (obviously), just click the Ignore button if that dialog appears.
3. With the affected VM selected in VBox Manager, click the Settings gear icon at the top.
4. Locate the Storage choice (4th down) on the left and click it. In the Storage Tree in the center you will see an IDE controller, click that. Now click the Add Hard Disk icon (which does not look like a CD, but sort of like a hard disk :-). A VBox dialog appears, click the Choose existing disk button. Navigate to the location of your moved .vdi file and double-click that file (the red box icon) in the Windows Explorer dialog, and click the OK button.
Done, your VM should start back up.