A coordinated continental‐scale field experiment across 31 sites was used to compare the biomass yield of monocultures and four species mixtures associated with intensively managed agricultural grassland systems. To increase complementarity in resource use, each of the four species in the experimental design represented a distinct functional type derived from two levels of each of two functional traits, nitrogen acquisition (N2‐fixing legume or nonfixing grass) crossed with temporal development (fast‐establishing or temporally persistent). Relative abundances of the four functional types in mixtures were systematically varied at sowing to vary the evenness of the same four species in mixture communities at each site and sown at two levels of seed density. Across multiple years, the total yield (including weed biomass) of the mixtures exceeded that of the average monoculture in >97% of comparisons. It also exceeded that of the best monoculture (transgressive overyielding) in about 60% of sites, with a mean yield ratio of mixture to best‐performing monoculture of 1·07 across all sites. Analyses based on yield of sown species only (excluding weed biomass) demonstrated considerably greater transgressive overyielding (significant at about 70% of sites, ratio of mixture to best‐performing monoculture = 1·18). Mixtures maintained a resistance to weed invasion over at least 3 years. In mixtures, median values indicate <4% of weed biomass in total yield, whereas the median percentage of weeds in monocultures increased from 15% in year 1 to 32% in year 3. Within each year, there was a highly significant relationship (P < 0·0001) between sward evenness and the diversity effect (excess of mixture performance over that predicted from the monoculture performances of component species). At lower evenness values, increases in community evenness resulted in an increased diversity effect, but the diversity effect was not significantly different from the maximum diversity effect across a wide range of higher evenness values. The latter indicates the robustness of the diversity effect to changes in species' relative abundances. Across sites with three complete years of data (24 of the 31 sites), the effect of interactions between the fast‐establishing and temporal persistent trait levels of temporal development was highly significant and comparable in magnitude to effects of interactions between N2‐fixing and nonfixing trait levels of nitrogen acquisition. Synthesis and applications. The design of grassland mixtures is relevant to farm‐level strategies to achieve sustainable intensification. Experimental evidence indicated significant yield benefits of four species agronomic mixtures which yielded more than the highest‐yielding monoculture at most sites. The results are relevant for agricultural practice and show how grassland mixtures can be designed to improve resource complementarity, increase yields and reduce weed invasion. The yield benefits were robust to considerable changes in the relative proportions of the four species, which is extremely useful for practical management of grassland swards.