In recent years, the optical Vernier effect has been demonstrated as an effective tool to improve the sensitivity of optical fiber interferometer-based sensors, potentially facilitating a new generation of highly sensitive fiber sensing systems. Previous work has mainly focused on the physical implementation of Vernier-effect-based sensors using different combinations of interferometers, while the signal demodulation aspect has been neglected. However, accurate and reliable extraction of useful information from the sensing signal is critically important and determines the overall performance of the sensing system. In this Letter, we, for the first time, propose and demonstrate that machine learning (ML) can be employed for the demodulation of optical Vernier-effect-based fiber sensors. ML analysis enables direct, fast, and reliable readout of the measurand from the optical spectrum, avoiding the complicated and cumbersome data processing required in the conventional demodulation approach. This work opens new avenues for the development of Vernier-effect-based high-sensitivity optical fiber sensing systems.