Deep learning has provided numerous breakthroughs in natural imaging tasks. However, its successful application to medical images is severely handicapped with the limited amount of annotated training data. Transfer learning is commonly adopted for the medical imaging tasks. However, a large covariant shift between the source domain of natural images and target domain of medical images results in poor transfer learning. Moreover, scarcity of annotated data for the medical imaging tasks causes further problems for effective transfer learning. To address these problems, we develop an augmented ensemble transfer learning technique that leads to significant performance gain over the conventional transfer learning. Our technique uses an ensemble of deep learning models, where the architecture of each network is modified with extra layers to account for dimensionality change between the images of source and target data domains. Moreover, the model is hierarchically tuned to the target domain with augmented training data. Along with the network ensemble, we also utilize an ensemble of dictionaries that are based on features extracted from the augmented models. The dictionary ensemble provides an additional performance boost to our method. We first establish the effectiveness of our technique with the challenging ChestXray-14 radiography data set. Our experimental results show more than 50% reduction in the error rate with our method as compared to the baseline transfer learning technique. We then apply our technique to a recent COVID-19 data set for binary and multi-class classification tasks. Our technique achieves 99.49% accuracy for the binary classification, and 99.24% for multi-class classification.