Olive leaves are an abundant by-product of olive oil production. Olive leaf extracts (OLEs) are rich in polyphenols, which can be used for health benefits. As polyphenols are the main antioxidant molecules in plants, plants typically increase their polyphenol content when exposed to drought stress. However, the phenolic profile of OLEs can vary in relation to the origin and variety of the plant material. In this work, olive leaf extracts from three different Italian olive cultivars (Giarraffa, Leccino, and Maurino) both exposed and not exposed to drought stress were studied in terms of antioxidant properties and profile, intestinal permeation, and protection against oxidative stress of human umbilical vein endothelial cells (HUVECs), since HUVECs are considered a model to study a wide range of diseases. OLEs from stressed Maurino and Giarraffa plants showed the highest increase in antioxidant capacity compared to controls. The phenolic profile of Maurino’ was mainly increased by water deficit, with a large increase in the compounds oleuropein and luteolin-7-O-rutinoside. All tested extracts exposed to a water deficit protected HUVECs against oxidative stress by reducing ROS production, and this effect was more pronounced in OLEs from Giarraffa and Maurino exposed to drought stress compared to all other extracts. Finally, OLE from the stressed Giarraffa group showed a higher apparent permeability of antioxidant molecules than that of Maurino.