Variational autoencoders (VAEs) are challenged by the imbalance between representation inference and task fitting caused by surrogate loss. To address this issue, existing methods adjust their balance by directly tuning their coefficients. However, these methods suffer from a tradeoff uncertainty, i.e., nondynamic regulation over iterations and inflexible hyperparameters for learning tasks. Accordingly, we make the first attempt to introduce an evolutionary VAE (eVAE), building on the variational information bottleneck (VIB) theory and integrative evolutionary neural learning. eVAE integrates a variational genetic algorithm (VGA) into VAE with variational evolutionary operators, including variational mutation (V-mutation), crossover, and evolution. Its training mechanism synergistically and dynamically addresses and updates the learning tradeoff uncertainty in the evidence lower bound (ELBO) without additional constraints and hyperparameter tuning. Furthermore, eVAE presents an evolutionary paradigm to tune critical factors of VAEs and addresses the premature convergence and random search problem in integrating evolutionary optimization into deep learning. Experiments show that eVAE addresses the KL-vanishing problem for text generation with low reconstruction loss, generates all the disentangled factors with sharp images, and improves image generation quality. eVAE achieves better disentanglement, generation performance, and generation-inference balance than its competitors. Code available at: https://github.com/amasawa/eVAE.