The combination of multilingual pre-trained representations and cross-lingual transfer learning is one of the most effective methods for building functional NLP systems for low-resource languages. However, for extremely low-resource languages without large-scale monolingual corpora for pre-training or sufficient annotated data for fine-tuning, transfer learning remains an understudied and challenging task. Moreover, recent work shows that multilingual representations are surprisingly disjoint across languages, bringing additional challenges for transfer onto extremely low-resource languages. In this paper, we propose MetaXL, a meta-learning based framework that learns to transform representations judiciously from auxiliary languages to a target one and brings their representation spaces closer for effective transfer. Extensive experiments on real-world low-resource languages -- without access to large-scale monolingual corpora or large amounts of labeled data -- for tasks like cross-lingual sentiment analysis and named entity recognition show the effectiveness of our approach. Code for MetaXL is publicly available at github.com/microsoft/MetaXL.