This paper presents a novel method for embedding transfer, a task of transferring knowledge of a learned embedding model to another. Our method exploits pairwise similarities between samples in the source embedding space as the knowledge, and transfers them through a loss used for learning target embedding models. To this end, we design a new loss called relaxed contrastive loss, which employs the pairwise similarities as relaxed labels for inter-sample relations. Our loss provides a rich supervisory signal beyond class equivalence, enables more important pairs to contribute more to training, and imposes no restriction on manifolds of target embedding spaces. Experiments on metric learning benchmarks demonstrate that our method largely improves performance, or reduces sizes and output dimensions of target models effectively. We further show that it can be also used to enhance quality of self-supervised representation and performance of classification models. In all the experiments, our method clearly outperforms existing embedding transfer techniques.