During the San Diego Comic-Con, Sony representatives officially announced that the PlayStation 4 console will natively support wireless headsets for PS3.
As a reminder, the standard PlayStation 4 bundle will include a wired mono headset that connects to the DualShock 4 controller, but if you have any wireless headset for PS3, you will have no problem using it.
Microsoft did not immediately decide to include a wired headset in the Xbox One package, and even so, this information is still not official.