AMD manufactures the system-on-chip used in Xbox Series X.
The Xbox Series X uses a custom AMD processor combining an eight-core Zen 2 CPU with a Radeon RDNA 2-based graphics processor. Microsoft designed the system specifications with AMD, allowing the console to use a single integrated chip rather than separate retail PC components.
This partnership continued a long Xbox hardware relationship. The original Xbox used an Nvidia graphics processor, while Xbox 360 used an ATI graphics processor after AMD acquired ATI. Later Xbox generations used custom AMD silicon for both central and graphics processing.
The answer is the chip manufacturer, not the console designer. Microsoft defines the Xbox Series X architecture and software platform, but AMD supplies the underlying custom silicon. Nvidia and Intel are major PC chip companies, yet neither manufactured the Series X system-on-chip.