You definitely need to call your insurance company and add him to your policy. Letting him drive without being listed is a real problem - if he gets in an accident, your insurer could deny the claim entirely because he wasn't disclosed as a regular driver. That's not just a technicality; it leaves you and him exposed financially. Most insurers require you to list all household members who have a license and regular access to the vehicle.
Yeah, the cost will go up, but it's worth getting a quote before you panic. Teenage drivers do bump the premium, but the increase varies a lot depending on your insurer, your location, and his driving record. Some companies offer discounts if he maintains good grades, takes a defensive driving course, or if the car has safety features. It's also worth shopping around - different insurers price teen drivers differently, so you might find better rates elsewhere. I'd contact your current company first, get the actual number, then check a couple of competitors to see where you stand.
The process is straightforward: call, give them his license info, and they'll recalculate your premium. Make sure this happens before he starts driving regularly, not after. It takes maybe 10 minutes on the phone.