In this paper, the three-body problem, the long-standing unsolved core puzzle in classical celestial mechanics, is taken as the targeted research object. Rooted strictly in the basic axiom system of Newtonian mechanics, it conducts rigorous mathematical derivation and systematic proof to formally propose a universally applicable gravitational superposition theorem. The theorem explicitly states that the total gravitational field generated at any arbitrary external spatial point by a gravitational system composed of finite mass points is completely equivalent to the gravitational field produced by a single mass point located exactly at the system’ centroid, with its total mass equal to the sum of all individual mass points in the system.Taking this newly proven theorem as the solid theoretical cornerstone, this research successfully achieves the dimensionality reduction mapping of the classical three-body problem into three mutually interrelated two-body motion frameworks at the level of dynamical equations. This breakthrough builds a self-consistent theoretical path with strict mathematical logic for the global analytical solution of the three-body system, fundamentally breaking through the long-term traditional academic view that "the general three-body system has no global analytical general solution". Furthermore, this theoretical framework can be extended to arbitrary N-body gravitational systems through strictly rigorous recursive derivation, laying a foundational theoretical support for reconstructing a complete and closed analytical system of classical many-body gravitational dynamics, covering both dynamical laws and gravitational potential energy structures.