Federated Graph Learning (FGL) has emerged as a compelling paradigm for collaboratively training a global model while preserving the privacy of multi-source graphs. Nonetheless, FGL faces a critical challenge of data heterogeneity, where semantic and structural discrepancies across clients significantly degrade its performance. Although existing methods attempt to calibrate client-specific graph distributions during the federated training, they inevitably fall short in aligning the optimization behaviors across clients due to dynamic parameter updates, thereby inducing a bottleneck in generalization improvement. To tackle this challenge, we propose a solution from a new perspective of prior refinement, which seeks to proactively harmonize client graph distributions before the federated training. In particular, we propose a Federated Graph Harmonization (FedGH) framework that exploits the generative strengths of graph diffusion models to perform prior refinement of local graphs. In a nutshell, FedGH designs a conditional diffusion mechanism on each client that synthesizes pseudo-graphs encapsulating both feature and structural priors, thereby facilitating explicit correction of inter-client distributional bias. On the server side, we employ the graph contrastive learning between various client-specific pseudo-graphs to incorporate the global information, subsequently guiding local data reconstruction. Importantly, model-agnostic FedGH can be seamlessly deployed as a plug-and-play module to be easily integrated with existing FGL architectures. Extensive experiments demonstrate that FedGH consistently outperforms state-of-the-art FGL baselines.