Increased biodiversity may improve ecosystem services, including herbage yield. A mixture experiment was carried out at five sites in Northern Europe and one in Canada to investigate whether mixtures of grasses and legumes would give higher herbage yield than monocultures. Resistance of the mixtures to weed invasion and nutritive value of the herbage were also investigated. The experimental layout followed a simplex design, where four species differing in specific functional traits, timothy (Phleum pratense L.), smooth meadow grass (Poa pratensis L.), red clover (Trifolium pratense L.) and white clover (Trifolium repens L.), were grown in monocultures and eleven different mixtures with systematically varying proportions of the four species. Positive diversity effects (DE) were observed, leading to greater herbage dry‐matter (DM) yield in mixtures than expected from species sown in monocultures. For centroid mixtures, the DE generated on average an additional 32, 25 and 21% of the DM yield than would be expected from the monocultures in the first, second and third year respectively. On average, the mixtures were 9, 15 and 7% more productive than the most productive monoculture (transgressive overyielding) in the first, second and third year respectively. These benefits persisted over the three harvest years of the experiment and were consistent among most sites. This positive effect was not accompanied by a reduction in herbage digestibility and crude protein concentration that is usually observed with increased DM yield. Mixtures also reduced the invasion of weeds to <5% of herbage yield compared to monocultures (10–60% of herbage yield).