In a series of three companion papers published in this Journal, we identify and validate the available thermal stress indicators (TSIs). In this first paper of the series, we conducted a systematic review (registration: INPLASY202090088) to identify all TSIs and provide reliable information regarding their use (funded by EU Horizon 2020; HEAT-SHIELD). Eight databases (PubMed, Agricultural and Environmental Science Collection, Web of Science, Scopus, Embase, Russian Science Citation Index, MEDLINE, and Google Scholar) were searched from database inception to 15 April 2020. No restrictions on language or study design were applied. Of the 879 publications identified, 232 records were considered for further analysis. This search identified 340 instruments and indicators developed between 200 BC and 2019 AD. Of these, 153 are nomograms, instruments, and/or require detailed non-meteorological information, while 187 can be mathematically calculated utilizing only meteorological data. Of these meteorology-based TSIs, 127 were developed for people who are physically active, and 61 of those are eligible for use in occupational settings. Information regarding the equation, operating range, interpretation categories, required input data, as well as a free software to calculate all 187 meteorology-based TSIs is provided. The information presented in this systematic review should be adopted by those interested in performing on-site monitoring and/or big data analytics for climate services to ensure appropriate use of the meteorology-based TSIs. Studies two and three in this series of companion papers present guidance on the application and validation of these TSIs, to guide end users of these indicators for more effective use.