Thermally conductive polymer composites hold great potential for thermal management applications in the electronics industry, but achieving metal‐like thermal conductivity (>200 W m−1 K−1) remains challenging due to the inevitable phonon scattering and the thermal resistance at filler‐filler and filler‐matrix interfaces. Herein, an efficient approach is presented to overcome this long‐standing barrier by designing a densified interconnecting filler framework, featuring a macro‐level carbon fiber (CF) array welded with a high‐quality, self‐assembled graphene network. In this framework, vertically aligned continuous CFs function as primary through‐plane thermal conduction paths, minimizing phonon scattering and thermal resistance. Meanwhile, the secondary graphene network interconnects the CFs into a more integrated and densified framework while introducing supplementary thermal conduction paths. Following polymer backfilling, the resulting epoxy nanocomposite exhibits an unprecedented through‐plane thermal conductivity of 262 W m−1 K−1 at a filler loading of 23.3 vol%, establishing a new benchmark among the thermally conducting polymer composites. When employed as a thermal interface material, this composite offers a 68.2% enhancement in cooling efficiency compared to standard commercial counterparts. Furthermore, the functional composite presents excellent Joule heating and interfacial adhesion properties, making it promising for thermal interface healing and multifunctional thermal management applications in complex environments.