International projections point to the growth in global production of sheep meat, mainly from developing countries. However, the exigencies of consumers on characterization of production systems, nutritional information, and sensorial analysis to target the preferences must be answered. The aim of this study was to characterize the meat quality and the global acceptance of Brazilian native ovine breeds and their crosses, and discuss these aspects on the current basis of human health and wellbeing. Three native breeds (Morada Nova, Rabo Largo, and Santa Inês) that were managed in semi-intensive systems and raised in semi-arid Brazilian regions were used. Chemical composition and fatty acid analysis, sensory evaluation and health indices were accessed. The combined effects of breed, sex and breed by sex interaction produced differentiation in meat fatty acid (FA) profiles. The cholesterol contents ranged between 51 and 59.1 mg/100 g. The Morada Nova lambs showed the lowest lipid content (1.93%). The Morada Nova x Rabo Largo crossbreed breed has the potential to increase the content of conjugated linoleic acid. The high content of α-linolenic acid, which is considered hypocholesterolemic, was responsible for better health indices. The moderate acceptability obtained in sensory traits is compatible with the requirements of the consumer market. The combination of nutritional and sensory traits associated with human health and wellbeing that is presented by these native ovine breeds qualifies them as a good choice of red meat to be included in a larger proportion in human food.