Basic bovine behavior is a crucial parameter influencing cattle domestication. In addition, behavior has an impact on cattle productivity, welfare and adaptation. The aim of the present study was to infer quantitative genetic and genomic mechanisms contributing to natural dual-purpose cow behavior in grazing systems. In this regard, we genotyped five dual-purpose breeds for a dense SNP marker panel from four different European countries. All cows from the across-country study were equipped with the same electronic recording devices. In this regard, we analyzed 97,049 longitudinal sensor behavior observations from 319 local dual-purpose cows for rumination, feeding, basic activity, high active, not active and ear temperature. According to the specific sensor behaviors and following a welfare protocol, we computed two different welfare indices. For genomic breed characterizations and multi-breed genome-wide association studies, sensor traits and test-day production records were merged with 35,826 SNP markers per cow. For the estimation of variance components, we used the pedigree relationship matrix and a combined similarity matrix that simultaneously included both pedigree and genotypes. Heritabilities for feeding, high active and not active were in a moderate range from 0.16 to 0.20. Estimates were very similar from both relationship matrix-modeling approaches and had quite small standard errors. Heritabilities for the remaining sensor traits (feeding, basic activity, ear temperature) and welfare indices were lower than 0.09. Five significant SNPs on chromosomes 11, 17, 27 and 29 were associated with rumination, and two different SNPs significantly influenced the sensor traits “not active” (chromosome 13) and “feeding” (chromosome 23). Gene annotation analyses inferred 22 potential candidate genes with a false discovery rate lower than 20%, mostly associated with rumination (13 genes) and feeding (8 genes). Mendelian randomization based on genomic variants (i.e., the instrumental variables) was used to infer causal inference between an exposure and an outcome. Significant regression coefficients among behavior traits indicate that all specific behavioral mechanisms contribute to similar physiological processes. The regression coefficients of rumination and feeding on milk yield were 0.10 kg/% and 0.12 kg/%, respectively, indicating their positive influence on dual-purpose cow productivity. Genomically, an improved welfare behavior of grazing cattle, i.e., a higher score for welfare indices, was significantly associated with increased fat and protein percentages.