The integration of high-κ dielectrics with two-dimensional (2D) semiconductors has long been limited by the low reactivity of their dangling-bond-free surfaces and the scalability issues of conventional deposition techniques. Here, we report a universal van der Waals (vdW) integration strategy using HfSe2 as a high-κ precursor that is dry-transferred onto MoS2 and WSe2 and fully converted into amorphous HfO2 via plasma oxidation, while preserving atomically flat vdW interfaces. The resulting HfO2/MoS2 and HfO2/WSe2 gate stacks exhibit suppressed interface trap densities (Dit ≈ 7-8 × 1010 cm-2 eV-1) and high dielectric constants (κ ≈ 23). MoS2 n-type field-effect transistors (nFETs) and WSe2 p-type field-effect transistors (pFETs) fabricated with this approach achieve nearly ideal subthreshold swing ( ≈ 60 mV/dec) and negligible hysteresis ( ≈ 3 mV). This scalable methodology enables the vertical integration of complementary logic, demonstrated by complementary FET inverters and ring oscillators, establishing a promising route toward three-dimensional, energy-efficient logic technologies.