  We consider the Cauchy problem for the defocusing energy-critical stochastic
nonlinear wave equations (SNLW) with an additive stochastic forcing on
$\mathbb{R}^{d}$ and $\mathbb{T}^{d}$ with $d \geq 3$. By adapting the
probabilistic perturbation argument employed in the context of the random data
Cauchy theory by B\'enyi-Oh-Pocovnicu (2015) and Pocovnicu (2017) and in the
context of stochastic PDEs by Oh-Okamoto (2020), we prove global well-posedness
of the defocusing energy-critical SNLW. In particular, on $\mathbb{T}^d$, we
prove global well-posedness with the stochastic forcing below the energy space.
