We show that the electromagnetic quantum vacuum plays a primary role in gravitation and cosmology. - Photons are local oscillations of the electromagnetic vacuum field guided by a non-local vector potential wave function - The vacuum electric permittivity and magnetic permeability are intrinsic properties of the electromagnetic vacuum. - We show that the electron-positron elementary charge derive naturally from the electromagnetic quantum vacuum - The masses of all particles (leptons, mesons, baryons) and antiparticles are quantum states of the elementary charges and their corresponding magnetic moments. We demonstrate the equivalence of Newton's gravitational law to Coulomb's electrostatic law. - The gravitational constant G is also related directly to the electromagnetic quantum vacuum putting in evidence the electromagnetic nature of gravity. - We show that G is the same for matter and antimatter but gravitational forces appear to be repulsive between particles and antiparticles since their masses bear opposite signs. Antimatter in universe contributes to the cosmic acceleration. - Dark Energy and Dark Matter might also originate from the electromagnetic quantum vacuum fluctuations. The calculated vacuum energy density, related to the cosmological constant contributing to the cosmic acceleration, is in good agreement with the astrophysical observations. - Under these conditions, the electromagnetic quantum vacuum might constitute the physical basis for a unified field theory.