The Southern Ocean exerts a disproportionate influence on marine ecosystems and the global carbon cycle through its control on net primary production (NPP) and biological carbon export. Marine NPP removes carbon dioxide through photosynthesis and supports marine food webs, including ecologically and economically important organisms such as Antarctic krill and whales. Climate-driven changes in Southern Ocean NPP therefore have important implications for ecosystem services and carbon-cycle feedbacks. However, projections of Southern Ocean NPP vary widely across Earth system models (ESMs), especially under the high-emission scenario (SSP5-8.5, Shared Socioeconomic Pathway 5-8.5). Here, we identify a robust emergent relationship between present-day environmental conditions and future Southern Ocean NPP changes across two generations of multi-model ensembles (CMIP5 and CMIP6). Using multi-decadal observational records to constrain this relationship, we reduce projection uncertainty by 37%, and find that the future NPP increase under SSP5-8.5 is likely smaller than indicated by the unconstrained ensemble (0.6±0.4 Pg C year^-1 and 0.3±0.3 Pg C year^-1 before and after constraint, respectively). Analysis of phytoplankton growth-limitation terms shows that the productivity increase is mainly linked to a weakening of temperature limitation, rather than systematic changes of iron or light limitation. This reduced productivity response has implications for Southern Ocean ecosystem change and the strength of the biological carbon pump under continued climate warming