Electroencephalogram (EEG), which directly reflects the emotional activity of the brain, has been increasingly utilized for emotion recognition. Most works exploit the spatial and temporal dependencies in EEG to learn emotional feature representations, but they still have two limitations to reach their full potential. First, prior knowledge is rarely used to capture the spatial dependency of brain regions. Second, the cross temporal dependency between consecutive time slices for different brain regions is ignored. To address these limitations, in this paper, we propose Variational Spatial and Gaussian Temporal (VSGT) graph models to investigate the spatial and temporal dependencies for EEG-based emotion recognition. The VSGT has two key components: Variational Spatial Encoder (VSE) and Gaussian Temporal Encoder (GTE). The VSE leverages the upper bound theorem to identify the dynamic spatial dependency based on prior knowledge by the variational Bayesian method. Besides, the GTE exploits the conditional Gaussian graph transform that computes comprehensive temporal dependency between consecutive time slices. Finally, the VSGT utilizes a recurrent structure to calculate the spatial and temporal dependencies for all time slices. Extensive experiments show the superiority of VSGT over state-of-the-art methods on multiple EEG datasets.