Additionally to Helmar's answer, one might add the following:

You don't need to transfer your whole account. Under Content and Devices > Settings > Country Settings, don't click the big change button, rather click the small link below and follow the instructions. That'll change your content-account to use the US-store. If you have to insert an address in the US, you're doing the wrong thing.

Edit: It looks like Amazon changed their UI. Now, when I go to Content and Devices, I only get a list of my content and no ore settings or country settings directly. Instead, At the top of the page, (having set my content to the US-Store) I get the following two messages:

You can manage your content and devices directly from Amazon.de. Learn more

Your default Kindle Store is currently set to Amazon.com. Go to the Manage Your Content and Devices page at Amazon.com.

The latter is irrelevant, but at the former, I get the option to Transfer your Kindle Account to Amazon.de. These links might be personalized. If you don't have these two messages at the beginning, try the latter link. You might have a message then.