Background: Olive leaves are a significant source of biophenols, which have a beneficial impact on cognitive performance. Objective: To examine, for the first time, in humans the effect of the daily consumption of a beverage containing olive leaf extract (OLE) versus a Mediterranean diet (MeDi) on patients diagnosed with mild Alzheimer’s Disease (AD), in addition to their regular treatment. Methods: A randomized clinical trial compared OLE’s effects on cognitive and functional performance in 55 mild AD patients. Each participant was randomly assigned to two groups: (1) Group 1 was given olive leaves for making a daily beverage and MeDi instructions through monthly diet programs; (2) Group 2 received only the MeDi instructions. After six months, all participants underwent a second neuropsychological evaluation. Results: Group 1 participants had statistically significantly higher MMSE scores compared to Group 2 with a p-value of 0.0135. Specifically, the mean MMSE difference in patients receiving OLE was close to 0, indicating no memory deterioration, whereas in controls it was −4.1, indicative of cognitive decline. The remaining neuropsychological assessments (FRSSD, FUCAS, ADAS-Cog, CDR, GDS, and NPI) revealed better results in the OLE group, except for GDS, which showed no change, but without statistically significant differences between the two groups.