At present the olive oil industry produces large amounts of secondary products once considered waste or by-products. In this paper, we present, for the first time, a new interesting olive by-product named “dried destoned virgin olive pomace” (DDVOP), produced by the pomace oil industry. The production of DDVOP is possible thanks to the use of a new system that differs from the traditional ones by having the dryer set at a lower temperature value, 350 °C instead of 550 °C, and by avoiding the solvent extraction phase. In order to evaluate if DDVOP may be suitable as a new innovative feeding integrator for animal feed, its chemical characteristics were investigated. Results demonstrated that DDVOP is a good source of raw protein and precious fiber; that it is consistent in total phenols (6156 mg/kg); rich in oleic (72.29%), linoleic (8.37%) acids and tocopherols (8.80 mg/kg). A feeding trial was, therefore, carried out on sheep with the scope of investigating the influence of the diet on the quality of milk obtained from sheep fed with DDVOP-enriched feed. The resulting milk was enriched in polyunsaturated (0.21%) and unsaturated (2.42%) fatty acids; and had increased levels of phenols (10.35 mg/kg) and tocopherols (1.03 mg/kg).