Basically one needs to create a custom background for a spinner. It should be something like this:
spinner_background.xml
<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item>
<layer-list>
<item>
<color
android:color="@android:color/white"/>
</item>
<item>
<bitmap
android:gravity="center_vertical|right"
android:src="@drawable/ic_arrow_drop_down_black_24dp"/>
</item>
</layer-list>
</item>
</selector>
Then create a custom style for your spinner, where you specify the above selector as background:
<style name="Widget.App.Spinner" parent="@style/Widget.AppCompat.Spinner">
<item name="overlapAnchor">true</item>
<item name="android:background">@drawable/spinner_background</item>
</style>
And finally in your app theme you should override two attributes if you want it to be applied all across your app:
<item name="spinnerStyle">@style/Widget.App.Spinner</item>
<item name="android:spinnerStyle">@style/Widget.App.Spinner</item>
And that's pretty much it.