Reviewing the metabolomics literature is becoming increasingly difficult because of the rapid expansion of relevant journal literature. Text-mining technologies are therefore needed to facilitate more efficient literature review. Here we contribute a standardised corpus of full-text publications from metabolomics studies and describe the development of two new metabolite named entity recognition (NER) methods. We introduce two deep learning methods for metabolite NER based on Bidirectional Long Short-Term Memory (BiLSTM) networks incorporating different transfer learning techniques. Our first model (MetaboListem) follows prior methodology using GloVe word embeddings. Our second model exploits BERT and BioBERT for embedding and is named TABoLiSTM (Transformer-Affixed BiLSTM). The methods are trained on a novel corpus annotated using rule-based methods, and evaluated on manually annotated metabolomics articles. MetaboListem (F1 score 0.890, precision 0.892, recall 0.888) and TABoLiSTM (BioBERT version: F1 score 0.909, precision 0.926, recall 0.893) have achieved state-of-the-art performance on metabolite NER. A corpus with $>$1,200 full-text Open Access metabolomics publications and $>$116,000 annotated metabolites was created. This work demonstrates that deep learning algorithms are capable of identifying metabolite names accurately and efficiently in text. The proposed corpus and NER algorithms can be used for metabolomics text-mining tasks such as information retrieval, document classification and literature-based discovery. The corpus and NER algorithms are freely available with detailed instructions from Github at https://github.com/omicsNLP/MetaboliteNER.