Large language model-based explainable recommendation (LLM-based ER) systems show promise in generating human-like explanations for recommendations. However, they face challenges in modeling user-item collaborative preferences, personalizing explanations, and handling sparse user-item interactions. To address these issues, we propose GaVaMoE, a novel Gaussian-Variational Gated Mixture of Experts framework for explainable recommendation. GaVaMoE introduces two key components: (1) a rating reconstruction module that employs Variational Autoencoder (VAE) with a Gaussian Mixture Model (GMM) to capture complex user-item collaborative preferences, serving as a pre-trained multi-gating mechanism; and (2) a set of fine-grained expert models coupled with the multi-gating mechanism for generating highly personalized explanations. The VAE component models latent factors in user-item interactions, while the GMM clusters users with similar behaviors. Each cluster corresponds to a gate in the multi-gating mechanism, routing user-item pairs to appropriate expert models. This architecture enables GaVaMoE to generate tailored explanations for specific user types and preferences, mitigating data sparsity by leveraging user similarities. Extensive experiments on three real-world datasets demonstrate that GaVaMoE significantly outperforms existing methods in explanation quality, personalization, and consistency. Notably, GaVaMoE exhibits robust performance in scenarios with sparse user-item interactions, maintaining high-quality explanations even for users with limited historical data.