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 meta-features. 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.