In this two-part article, we propose elastic models of disordered alloys to study the statistical properties of the random displacement and stress fields emerging from the random distributions of atoms of different sizes. In Part I, we presented realand Fourier-space approaches enabling to obtain the amplitude of the fluctuations through the mean square displacements and stresses. In the present Part II, we extend the Fourier approach to address spatial correlations. We show that, even if the alloy is fully disordered and elastically isotropic, correlations are highly anisotropic. Our continuum predictions are validated by comparisons with atomistic models of random alloys. We also discuss the consequence of displacement correlations on finite size effects in atomistic calculations and on diffuse X-ray and neutron scattering experiments and the possible implications of stress correlations on dislocation behavior.