This study provides new insights on the conditions of melt generation and of magma transport and storage beneath Tristan da Cunha Island in the South Atlantic. Situated at the seaward end of the Walvis Ridge-guyot hotspot track, this island is related to the evolving magmatic system of the Tristan plume. Much is known about the geochemical and isotopic composition of the alkaline lavas on Tristan, but the pressure–temperature conditions of the hotspot magmas are under-explored. This contribution reports new data from a suite of 10 samples collected during a geologic–geophysical expedition in 2012. The focus of this study is on the least-evolved, phenocryst-rich basanite lavas but we also included a sample of trachyandesite lava erupted in 1961. Mineral-melt equilibrium thermobarometry uses the composition of olivine, clinopyroxene and plagioclase phenocrysts. In addition to bulk-rock data we also analysed olivine-hosted melt inclusions for the P–T calculations. The results for olivine-melt and clinopyroxene-melt calculations suggest crystallization conditions of around 1200–1250 °C and 0.8–1.3 GPa for the least-evolved magmas (ankaramitic basanites). Combined with seismological evidence for a Moho depth of about 19 km, these results imply magma storage and partial crystallization of Tristan magmas in the uppermost mantle and at Moho level. The trachyandesite yielded values of about 1000 °C and 0.2–0.3 GPa (6 to 10 km depth), indicating further crystallization within the crust. Constraints on the depth and degree of melting at the source of Tristan basanites were derived from REE inverse modelling using our new trace element data. The model predicts 5% melt generation from a melting column with its base at 80–100 km and a top at 60 km, which is consistent with the lithospheric thickness resulting from cooling models and seismological observations. The thermobarometry and melting models combined suggest a mantle potential temperature of about 1360 °C for the Tristan hotspot.