In this paper, we study the problem of unifying knowledge from a set of classifiers with different architectures and target classes into a single classifier, given only a generic set of unlabelled data. We call this problem Unifying Heterogeneous Classifiers (UHC). This problem is motivated by scenarios where data is collected from multiple sources, but the sources cannot share their data, e.g., due to privacy concerns, and only privately trained models can be shared. In addition, each source may not be able to gather data to train all classes due to data availability at each source, and may not be able to train the same classification model due to different computational resources. To tackle this problem, we propose a generalisation of knowledge distillation to merge HCs. We derive a probabilistic relation between the outputs of HCs and the probability over all classes. Based on this relation, we propose two classes of methods based on cross-entropy minimisation and matrix factorisation, which allow us to estimate soft labels over all classes from unlabelled samples and use them in lieu of ground truth labels to train a unified classifier. Our extensive experiments on ImageNet, LSUN, and Places365 datasets show that our approaches significantly outperform a naive extension of distillation and can achieve almost the same accuracy as classifiers that are trained in a centralised, supervised manner.