This study focused on the volatile changes in cv. Verdeal Transmontana throughout the entire olive oil processing chain, from the drupe to olive oil storage up to 12 months, while correlating it with quality parameters and sensory quality. During crushing and malaxation, the volatiles formed were mainly “green-leaf volatiles” (GLVs), namely (E)- 2-hexenal, hexanal, and 1-hexanol. Centrifugation and clarification steps increased the total volatile amounts to 130 mg kg−1. However, clarification also increased nonanal and (E)-2-decenal contents, two markers of oxidation, with a noticeable loss of phenolic compounds and oxidative stability. During storage, the total volatile amounts reduced drastically (94% at 12 months after extraction), together with the positive sensory attributes fruity, green, bitter, and pungent. Despite being classified as extra-virgin after one year of storage, peroxides and conjugated dienes were significantly higher while there was a reduction in antioxidant capacity as well as in phenolic compounds (less 50%) and oxidative stability (57%). The present work allowed concluding that the extraction process modulates the volatile composition of olive oil, with a concentration of volatiles at the clarification step. During storage, volatiles are lost, mainly eight months after extraction, leading to the loss of important sensory attributes.