This paper introduces GRANNITE, a GPU-accelerated novel graph neural network (GNN) model for fast, accurate, and transferable vector-based average power estimation. During training, GRANNITE learns how to propagate average toggle rates through combinational logic: a netlist is represented as a graph, register states and unit inputs from RTL simulation are used as features, and combinational gate toggle rates are used as labels. A trained GNN model can then infer average toggle rates on a new workload of interest or new netlists from RTL simulation results in a few seconds.