Improving the thermal performance of the building envelope by enhancing the thermal insulation has been acknowledged as a highly effective way to achieve energy efficiency in buildings. Aerogel-based materials are considered one of the most promising thermal insulation materials for building applications because of their ultra-low thermal conductivity. In this study, the hygrothermal properties of two types of silica aerogel insulation composites are experimentally investigated, and their structural characteristics are further analyzed. The hygrothermal performance of the building envelope externally insulated by the silica aerogel composites is evaluated in different climates by the 3D heat, air, and moisture (HAM) simulations. The multidimensional effect at the thermal bridge of the building envelope is also evaluated. The results show that the silica aerogel insulation composites possess exceptional thermal conductivity, high water vapor permeability, and low moisture sorption. The 3D HAM model gives a more accurate insight into the thermal and moisture behaviors at the complex-structured thermal bridge sections. The silica aerogel insulation systems exhibit an excellent hygrothermal performance compared to the traditional insulation systems, especially in the cold climate zone. Specifically, the silica aerogel insulation systems can significantly improve the inner surface temperature and reduce the inner surface relative humidity of the building envelope with the same thickness as the traditional expanded polystyrene (EPS) and extruded polystyrene (XPS) insulations, thus lessening the mold growth risk and surface condensation.