Set Android to update only via WiFi? I own an Android phone (a Nexus 5, so it's "standard" Android) and use it with a very limited data plan. Sometimes it downloads huge updates over the mobile network, even though it's at home and could use our Wi-Fi.

I haven't caught it in the act, so I don't know if the updates are for the operating system itself or the apps.

Is there a setting I can use to configure the phone to download software updates exclusively via WiFi?
Yes. Probably, these are app's update, because if they are OS updates you would be asked to restart your device or install the update. To avoid auto update from app's:In the Play store app, swipe from the left edge to the right. Go to settings. Under the "General" list, select "Update app's automatically"and mark with a dot "Only through Wi-Fi"