Ovarian cancer is the most lethal cancer of the female reproductive organs. There are $5$ major histological subtypes of epithelial ovarian cancer, each with distinct morphological, genetic, and clinical features. Currently, these histotypes are determined by a pathologists microscopic examination of tumor whole-slide images (WSI). This process has been hampered by poor inter-observer agreement (Cohens kappa $0.54$-$0.67$). We utilized a textit{two}-stage deep transfer learning algorithm based on convolutional neural networks (CNN) and progressive resizing for automatic classification of epithelial ovarian carcinoma WSIs. The proposed algorithm achieved a mean accuracy of $87.54%$ and Cohens kappa of $0.8106$ in the slide-level classification of $305$ WSIs; performing better than a standard CNN and pathologists without gynecology-specific training.