Uncertainty is an important consideration in structural design and optimization to produce robust and reliable solutions. This paper introduces an efficient and accurate approach to robust structural topology optimization. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This new approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level-set-based topology optimization method are then used to demonstrate the proposed approach.