We provide a quantum field theoretic derivation of Einstein's Weak Equivalence Principle of general relativity using a new quantum gravity theory proposed by the authors called Electro-Magnetic Quantum Gravity or EMQG (ref. 1). EMQG is based on a new theory of inertia (ref. 5) proposed by R. Haisch, A. Rueda, and H. Puthoff (which we modified and called Quantum Inertia). Quantum Inertia states that classical Newtonian Inertia is a property of matter due to the strictly local electrical force interactions of each of the (electrically charged) elementary particles of the mass (masseon particles) with the surrounding (electrically charged) virtual particles (virtual masseons) of the quantum vacuum. The sum of all the tiny electrical forces (photon exchanges with the vacuum particles) that originate in each charged elementary particle of the accelerated mass is the source of the total inertial force of a mass which opposes accelerated motion in Newton's law 'F = MA'. We invoked Einstein's principle of equivalence of inertial and gravitational mass to understand the origin of gravitational mass from the perspective of quantum inertia. We found that gravity also involves the same 'inertial' electrical force component that exists in inertial mass. We propose that Einstein's general relativistic Weak Equivalence Principle originates from common 'lower level' quantum vacuum processes occurring in both gravitational mass and inertial mass in accordance with the principles of quantum field theory.