Organofluorine compounds are finding increasing application in a variety of fields such as pharmaceutical, agrochemical, and material sciences. However, given the scarcity of fluorine-containing natural products, advancement in this area depends almost entirely on the development of new synthetic methodologies. In this article, we present the synthesis of a series of previously undescribed (E)-β-fluorovinyl sulfones via a simple copper-catalyzed addition of hydrogen fluoride to alkynyl sulfone starting materials in varying yields and E/Z selectivities. The hydrogenation of these products was also explored and compared with the hydrogenation of the related Z isomers. These new products may find interesting applications, given the versatility of vinyl sulfones in chemical synthesis and the unique properties of vinyl fluorides in biological settings.