Can I connect headphones that are not the Xbox stereo headset to the Xbox One?

Solution 1:

Those headphones appear to come with a 3.5mm audio jack cable. I use to use a pair of JBL headphones (JBL Synchros S500) with my Xbox One by simply connecting the headphones to the input on the controller using said jack. The inline microphone worked to chat with friends and the game audio also came through. I'm unsure if your microphone will work since it's not inline, but rather built into the headphones.

See this help page from Xbox. There are two common standards for 3.5mm audio jacks, Cellular Telecommunications Industry Association (CTIA) and Open Mobile Terminal Platform (OMTP). The Xbox One controllers audio jack input is CTIA, although with an adapter, you might be able to get an OMTP jack to work as well. When I use to use my JBL headphones, I didn't need any adapters, so its possible you won't either.