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 reviews. Here we contribute a standardised corpus of full-text publications from metabolomics studies and describe the development of two metabolite named entity recognition (NER) methods. These methods are based on Bidirectional Long Short-Term Memory (BiLSTM) networks and each incorporate different transfer learning techniques (for tokenisation and word embedding). 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 training corpus with full-text sentences from $>$1,000 full-text Open Access metabolomics publications with 105,335 annotated metabolites was created, as well as a manually annotated test corpus (19,138 annotations). 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. They are available from https://github.com/omicsNLP/MetaboliteNER.