With the desired tool window selected, press Alt+Minus to bring up the tool window menu. Press Down Arrow to select the Move command and hit Enter. Now, you can control the tool window with the arrow keys.
To dock, simply use the arrow keys to the desired dock target and hit Enter.
Reposted from Did you know… How to drag a tool window around using the keyboard? – #005 by Sara Ford, author of Microsoft Visual Studio Tips
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