Developing materials to serve as plasma-facing components (PFCs) in the extreme environment of nuclear fusion reactors is a major obstacle to be overcome toward the practical realization of fusion energy. Tungsten (W) is the chosen PFC material for the divertor of the International Thermonuclear Experimental Reactor (ITER) due to its exceptional thermomechanical properties. However, under expected typical operating conditions, a fragile nanofiber-like crystalline structure, known as “fuzz”, grows on the tungsten surface and poses a major operational challenge for ITER. Over the past two decades, numerous simulation studies have attempted to elucidate the mechanism of fuzz formation. Nevertheless, conducting simulations capable of accessing the experimentally relevant length and time scales for fuzz formation, on the order of micrometers and hours, remains an extremely challenging task. Toward this end, we have developed a 3D hierarchical continuum-scale model with atomistically derived constitutive information to simulate the surface morphological response of the helium plasma-irradiated tungsten and the onset of fuzz formation. Our model accounts for stress-induced surface diffusion, where the stress originates from over-pressurized helium bubbles in the near-surface region of the PFC material, and migration of W self-interstitial atoms toward the PFC surface. The model has been implemented numerically by combining Fourier spectral methods with front tracking techniques and validated by comparisons of its predictions with experimental data. We have studied systematically the effects on PFC tungsten surface morphological response of raising the surface temperature, softening of the tungsten elastic moduli due to the implanted helium, crater formation on the PFC surface due to bubble bursting, and surface vacancy-adatom pair formation during plasma exposure and established that all these factors accelerate the growth rate of the nanotendrils emanating from the tungsten surface. Using surface morphological stability analysis, we have shown that nanotendril formation on the PFC surface is the outcome of a stress-driven surface morphological instability. Furthermore, we have shown that fine-scale features (on the order of 100 nm) appearing on the PFC surface originate from surface craters formed as a result of bubble bursting and explained the experimentally observed formation of preferentially aligned stripe patterns on the PFC surface.