Composites based on Ce or Zr oxides (MeO₂) are highly demanded materials for energy, electronics, catalysis, and nanophotonics, but their development is hampered by high energy costs, difficulties in synthesis, and the lack of sound pressing and sintering modes for nanostructured powders. In this study, a method for producing composite powders based on oxygen-free graphene and MeO₂ for ceramics with a wide range of applications is proposed. The method is a combination of sol–gel and sonochemical techniques, allowing for the synthesis of hybrid structures with a uniform distribution of components in volume at the nanolevel. The developed hybrid structures consist of ceria or zirconia crystallites with dimensions of 6-14 nm, incorporated into graphene sheets several nm thick. Theoretically substantiated mechanisms for the formation of graphene suspensions, graphene–MeO₂ composites, and sintering of nanostructured hybrid powders are proposed based on the obtained experimental data. The positive effect of graphene on the microstructure of ceramics was determined: the use of a hybrid graphene–ZrO₂ powder makes it possible to obtain dense (98%), fine-grained ceramics with high structural homogeneity using the SPS method. It was shown that oxygen-free graphene on the surface of MeO₂ crystallites promotes the acceleration of surface exchange processes involving oxygen, which makes the developed composites promising raw materials for new electrical devices and catalysts. It was determined that graphene sheets and the method of their inclusion in the hybrid structure affect the activation energy of sintering and the mass transfer mechanism. The results of this study can be used as a basis for a technological process covering all stages, from obtaining initial solutions and colloids to sintered ceramics.