Temporal Knowledge Graph (TKG) reasoning seeks to predict future events by analyzing historical data, where the effective leverage of both local and global historical facts proves crucial. Existing approaches employ graph neural networks (GNNs) and recurrent neural networks (RNNs) for local evolution patterns, complemented by statistical methods to enhance attention to global facts, demonstrating efficient predictive capabilities. However, traditional GNNs, constrained by their low-order neighborhood aggregation design, inherently fail to model potential high-order dependencies among facts. Furthermore, existing global history modeling approaches may introduce irrelevant historical information that interferes with prediction tasks. To address these limitations, we propose a Dual History-aware HyperGraph Network for TKG reasoning, namely DHHGN. Specifically, for local history modeling, we design a hybrid hypergraph-graph joint recurrent convolution module that simultaneously captures low-order neighborhood information and high-order interaction patterns among entities, employing a gating mechanism to adaptively blend their contributions. For global history modeling, we propose a dual history enhancement module that amplifies attention on pivotal historical facts while ensuring holistic integration of all historical contexts. Extensive experiments on four public benchmarks validate that DualHist-HGN consistently outperforms existing state-of-the-art methods across TKG reasoning tasks.