Neuroimaging data acquired using multiple scanners or protocols are increasingly available. However, such data exhibit technical artifacts across batches which introduce confounding and decrease reproducibility. This is especially true when multi-batch data are analyzed using complex downstream models which are more likely to pick up on and implicitly incorporate batch-related information. Previously proposed image harmonization methods have sought to remove these batch effects; however, batch effects remain detectable in the data after applying these methods. We present DeepComBat, a deep learning harmonization method based on a conditional variational autoencoder and the ComBat method. DeepComBat combines the strengths of statistical and deep learning methods in order to account for the multivariate relationships between features while simultaneously relaxing strong assumptions made by previous deep learning harmonization methods. As a result, DeepComBat can perform multivariate harmonization while preserving data structure and avoiding the introduction of synthetic artifacts. We apply this method to cortical thickness measurements from a cognitive-aging cohort and show DeepComBat qualitatively and quantitatively outperforms existing methods in removing batch effects while preserving biological heterogeneity. Additionally, DeepComBat provides a new perspective for statistically motivated deep learning harmonization methods.