I'm not sure when the feature I use was added to the Android SDK but there is a simple solution that does exactly what the OP is looking for:
As expected, set layout:width and layout:height to fill_parent.
As another responder mentioned correctly, use src to find your image, not background.
However instead of trying scaleType of fit_xy (which finds the narrowest side to fit into the view rather than the longest side), use scaleType of centerCrop.
centerCrop will center and fill in the viewport while retaining aspect ratio.
Hope this helps! I used it for the webView loading overlay of a commercial app I developed for my current employer.
Copy/paste solution: in your activity XML file, add the following lines:
<ImageView
android:id="@+id/logo"
android:layout_width="wrap_content"
android:layout_height="fill_parent"
android:scaleType="centerCrop"
android:src="@drawable/your_image_name"
/>