How can I send VBoxHeadless to the background so I can close the Terminal?

Just found a solution here: Starting the the virtual machine with VBoxManage instead of VBoxHeadless solves my problem:

VBoxManage startvm <uuid|vmname> --type headless

For example, if your VM's name was Ubuntu and it had a UUID of 865b2700-471a-11e4-916c-0800200c9a66, you can run:

VBoxManage startvm Ubuntu --type headless

or

VBoxManage startvm 865b2700-471a-11e4-916c-0800200c9a66 --type headless

Note: If the name of your VM contains spaces, wrap the name in quotes (e.g. "My Ubuntu").

The machine goes nicely into the background. Now I can control the virtual machine with VBoxManage controlvm poweroff/pause/reset (section 3.3).