The development of monolingual language models for low and mid-resource languages continues to be hindered by the difficulty in sourcing high-quality training data. In this study, we present a novel cross-lingual vocabulary transfer strategy, trans-tokenization, designed to tackle this challenge and enable more efficient language adaptation. Our approach focuses on adapting a high-resource monolingual LLM to an unseen target language by initializing the token embeddings of the target language using a weighted average of semantically similar token embeddings from the source language. For this, we leverage a translation resource covering both the source and target languages. We validate our method with the Tweeties, a series of trans-tokenized LLMs, and demonstrate their competitive performance on various downstream tasks across a small but diverse set of languages. Additionally, we introduce Hydra LLMs, models with multiple swappable language modeling heads and embedding tables, which further extend the capabilities of our trans-tokenization strategy. By designing a Hydra LLM based on the multilingual model TowerInstruct, we developed a state-of-the-art machine translation model for Tatar, in a zero-shot manner, completely bypassing the need for high-quality parallel data. This breakthrough is particularly significant for low-resource languages like Tatar, where high-quality parallel data is hard to come by. By lowering the data and time requirements for training high-quality models, our trans-tokenization strategy allows for the development of LLMs for a wider range of languages, especially those with limited resources. We hope that our work will inspire further research and collaboration in the field of cross-lingual vocabulary transfer and contribute to the empowerment of languages on a global scale.