It was confirmed by Microsoft that every Xbox One Controller will be compatible with Xbox Series X; including version Elite and the Adaptive Controller, and also all controls that are manufactured by third parties. Compatibility goes to all games of the next generation.
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About Xbox One Controller Backward Compatibility for Xbox Series X Controller
Microsoft has also revealed that the Xbox Series X controllers will be backwards compatible, working on the Xbox One Controller and Windows computers, in addition to the devices Android e iOS, and also with the xCloud.
The announcement came shortly after rival company Sony announced the Dualshock 4 will not work on PlayStation 5 games. Of course, next generation games will be optimized for your haptic feedback from Dualense, which is Sony's justification for the lack of compatibility. Sony also said in its official blog that will talk a little more about the compatibility of PS4 accessories for PS5 on your State of Play event.
Both consoles still do not have an official release date set, but both are being promised for the end of the year 2020 and already have some very interesting details revealed.