I wrote an app to do it, so that it can be done by ADB with no need to touch the device:
adb install the-app.apk
adb shell am broadcast -a com.blundell.app.SET_WALLPAPER -n com.blundell.app/.SetWallpaper
adb uninstall com.blundell.app
The app:
Manifest:
<?xml version="1.0" encoding="utf-8"?>
<manifest
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    package="com.blundell.app"
    >
    <uses-permission android:name="android.permission.SET_WALLPAPER"/>
    <application
        android:allowBackup="false"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:supportsRtl="true"
        tools:ignore="GoogleAppIndexingWarning"
        >
        <receiver
            android:name=".SetWallpaper"
            tools:ignore="ExportedReceiver"
            >
            <intent-filter>
                <action android:name="com.blundell.app.SET_WALLPAPER"/>
            </intent-filter>
        </receiver>
    </application>
</manifest>
No Activities.
Broadcast Receiver:
class SetWallpaper : BroadcastReceiver() {
    override fun onReceive(context: Context?, intent: Intent?) {
        WallpaperManager.getInstance(context).setResource(R.raw.wallpaper)
    }
}
That's it!
And the wallpaper itself lives in the /res/raw/ directory. 
You could also pass the wallpaper location through the broadcast intent if you wanted.