In this article, we propose and solve a robust control problem (RCP) for inverter-based resources (IBRs) under grid-forming operation to regulate the voltage and frequency. One major challenge is to mitigate the effect of unmeasurable load current disturbance and grid and load parametric uncertainties. Moreover, strong coupling between the state variables on both the ac and dc sides, as well as between the modulating control input and the frequency impose additional challenges. To address these challenges, first, an RCP is solved at the high level via transformation into an equivalent, but more tractable, optimal control problem (OCP). Then, in the middle layer, a voltage control law is designed on the one side, and a frequency control law on the other side. Finally, an inverter filter current controller is designed to complete the controller design. Theoretical results are derived to provide stability guarantees for the resulting closed-loop system. Specifically, we show that the inverter current injection error is dissipative, the frequency error is semi-globally asymptotically stable, and the inverter terminal voltage error is globally asymptotically stable, all with provided sufficient conditions. Numerical simulation experiments are used to validate the theoretical claims. Furthermore, the developed controller is compared with existing work in the literature to show the efficacy of the proposed approach.