Telling my supervisor about my medical condition

Contact the disability center first.

You haven't listed a location, but most developed nations have laws prohibiting discrimination against individuals with disabilities, and mandating reasonable accommodations for their disabilities. The university disability office will likely have a better understanding of the university's policies and procedures as well as what reasonable accommodations you're entitled to than a random professor will (unless that's their research area or something). Additionally, helping you is literally their job, so you might as well take advantage of their services; it's not going to cost you or your lab/work group anything to do so, after all, and they should keep the contents of your communications with them private.

I will go against the other answers which unanimously suggest to talk to the disability centre first, and say that it depends.

It strongly depends on where you are, and on your relationship with your supervisor. I don't think anyone here can give you a definitive answer without a good understanding of your unique situation.

Your supervisor could be your best ally in navigating the bureaucracy at your institution, and finding a way to extend your funding if necessary. In a well-functioning research group, your supervisor would be your best ally, and could tell you what to do exactly to reach the best outcome. Of course, this is not always the case, which is why I said that it depends. I will just say that if you can expect the disability centre to give you more support than your supervisor, or even support you against your supervisor, that is a very sad state of affairs. It does happen though, which is why you need to make this call yourself.

It sounds like you have already decided to tell him one way or another, and the question is if you should speak to the disability office first. The disability office might have something helpful to add, so it should not hurt to speak to them first.

If there is any chance you might have seizures in the future, you should probably tell people you work with how they should react. Many faculty will call emergency services if they notice someone is having a seizure; if you don't want that to happen, say so.