Most game consoles don't support VPN apps and don't offer users the option to set up VPNs manually. That means you'll either have to set up a VPN on a wi-fi router or use a smart DNS proxy instead.
In either case, ExpressVPN fits the bill. It makes excellent router firmware for a select few router models that's far easier and more feature-rich than what you'll get on open-source alternatives. Every subscription also comes with the MediaStreamer smart DNS service, which you can set up on some game consoles, including Xbox and PlayStation.