Transfer learning aims to improve performance on a target task by utilizing previous knowledge learned from source tasks. In this paper we introduce a novel heterogeneous transfer learning technique, Feature-Space Remapping (FSR), which transfers knowledge between domains with different feature spaces. This is accomplished without requiring typical feature-feature, feature instance, or instance-instance co-occurrence data. Instead we relate features in different feature-spaces through the construction of metafeatures. We show how these techniques can utilize multiple source datasets to construct an ensemble learner which further improves performance. We apply FSR to an activity recognition problem and a document classification problem. The ensemble technique is able to outperform all other baselines and even performs better than a classifier trained using a large amount of labeled data in the target domain. These problems are especially difficult because, in addition to having different feature-spaces, the marginal probability distributions and the class labels are also different. This work extends the state of the art in transfer learning by considering large transfer across dramatically different spaces.