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The commissioning, development and results of an Electro-Optic Beam Position Monitor (EO-BPM) prototype installed in the CERN Super Proton Synchrotron (SPS) are reported in this thesis. This technology is a diagnostic technique that aims to be capable of measuring the transverse intra-bunch position in 1 ns proton bunches with a time resolution less than 100 ps, in order to achieve the requirements of the High Luminosity Large Hadron Collider (HL-LHC). The thesis details the mechanism that generates the electro-optic signal that results from the interaction of the Coulomb field with a lithium niobate crystal via the Pockels effect. The theoretical background leads to the introduction of the EO-BPM concept based on vacuum-integrated EO crystals in the context of the SPS machine. In conjunction with this, an analytical framework has been developed to estimate the EO pickup signal for the SPS beam parameters. This study also presents two different opto-mechanical pickup designs, pickup zero and one. Numerical electromagnetic simulations have been carried out to predict, more precisely, the performance of both proposals in relation to the modulating field. In addition, a detailed description of the experimental optical setup adjacent to the prototype and the acquisition system is presented. Further simulations have been applied to incorporate the response of the detection system to calculate the final signal delivered by the prototype. Results from measurements in December 2016 for pickup zero and over the summer 2017 for pickup one are reported and constitute the first detection ever of a proton beam by electro-optic means. Analysis verifies that the signal at a radial distance of 66.5mm scales correctly as a function of the beam conditions and the pickup model, and is also sensitive to the beam transverse position. These results provide the first proof of concept, in preparation for future developments of the technology towards the LHC upgrade.