International audience Marine primary production is a fundamental component of the Earth system, providing the main source of food and energy to the marine food web, and influencing the concentration of atmospheric CO$_2$ (refs. 1,2). Earth system model (ESM) projections of global marine primary production are highly uncertain with models projecting both increases (refs. 3,4) and declines of up to 20% by 2100 (refs. 5,6) This uncertainty is predominantly driven by the sensitivity of tropical ocean primary production to climate change, with the latest ESMs suggesting twenty-first-century tropical declines of between 1 and 30% (refs 5,6). Here we identify an emergent relationship (refs. 7-11) between the long-term sensitivity of tropical ocean primary production to rising equatorial zone sea surface temperature (SST) and the interannual sensitivity of primary production to El Niño/Southern Oscillation (ENSO)-driven SST anomalies. Satellite-based observations of the ENSO sensitivity of tropical primary production are then used to constrain projections of the long-term climate impact on primary production. We estimate that tropical primary production will decline by 3 ± 1% per kelvin increase in equatorial zone SST. Under a business-as-usual emissions scenario this results in an 11 ± 6% decline in tropical marine primary production and a 6 ± 3% decline in global marine primary production by 2100.