Plant–soil feedbacks (PSFs) have gained attention for their role in plant community dynamics, but their role in productivity has been overlooked. We developed and tested a biomass-specific, multi-species model to examine the role of PSFs in diversity–productivity relationships. The model predicts a negative relationship between PSFs and overyielding: plants with negative PSFs grow more in communities than in monoculture (i.e. overyield), and plants with positive PSFs grow less in communities than in monoculture (i.e. underyield). This effect is predicted to increase with diversity and saturate at low species richness because the proportion of ‘self-cultivated’ soils rapidly decreases as species are added to a community. Results in a set of glasshouse experiments supported model predictions. We found that PSFs measured in one experiment were negatively correlated with overyielding in three-species plant communities measured in a separate experiment. Furthermore, when parametrized with our experimental PSF data, our model successfully predicted species-level overyielding and underyielding. The model was less effective at predicting community-level overyielding and underyielding, although this appeared to reflect large differences between communities with or without nitrogen-fixing plants. Results provide conceptual and experimental support for the role of PSFs in diversity–productivity relationships.