If I uninstall the DxO software from my current computer, will that automatically release the activation for use on my new computer?

This information applies to version(s): 1, 2, 3, 4, 5, 6

No, after uninstalling the DxO software from your computer, you will need to contact support and tell them it has been removed. At that time, they can release the activation for use on your new computer. You can contact customer support here.