Skyrmions are whirl-like topological spin objects with high potential for future magnetic data storage. A fundamental question that is relevant to both basic research and application is whether ferroelectric (FE) polarization can be associated with skyrmions' magnetic texture and whether these objects can be manipulated by electric fields. We study the interplay between magnetism and electric polarization in the lacunar spinel GaV₄S₈, which undergoes a structural transition associated with orbital ordering at 44 K and reveals a complex magnetic phase diagram below 13 K, including ferromagnetic, cycloidal, and Néel-type skyrmion lattice (SkL) phases. We found that the orbitally ordered phase of GaV₄S₈ is FE with a sizable polarization of ∼1 mC/cm2. Moreover, we observed spin-driven excess polarizations in all magnetic phases; hence, GaV₄S₈ hosts three different multiferroic phases with coexisting polar and magnetic order. These include the SkL phase, where we predict a strong spatial modulation of FE polarization close to the skyrmion cores. By taking into account the crystal symmetry and spin patterns of the magnetically ordered phases, we identify exchange striction as the main microscopic mechanism behind the spin-driven FE polarization in each multiferroic phase. Because GaV₄S₈ is unique among known SkL host materials owing to its polar crystal structure and the observed strong magnetoelectric effect, this study is an important step toward the nondissipative electric field control of skyrmions.