Dense retrieval (DR) has become a mainstream approach to information seeking, where a system is required to return relevant information to a user query. In real-life applications, typoed queries resulting from the users’ mistyping words or phonetic typing errors exist widely in search behaviors. Current dense retrievers experience a significant drop in retrieval effectiveness when they encounter typoed queries. Therefore, the search system requires the extra introduction of spell-checkers to deal with typos and then applies the DR model to perform robust matching. Herein, we argue that directly conducting the typos correction training would be beneficial to make an end-to-end retriever against misspellings. To this end, we propose a novel approach that can facilitate the incorporation of the spelling correction objective into the DR model using the encoder-decoder architecture. During typos correction training, we also develop a prompt-based augmentation technique to enhance the DR space alignment of the typoed query and its original query. Extensive experiments demonstrate that the effectiveness of our proposed end-to-end retriever significantly outperforms existing typos-aware training approaches and sophisticated training advanced retrievers. Our code is available at https://github.com/striver314/ToCoTR.