Storage technology selection is a very important design decision that greatly affects the future performance of a warehouse; for example, it greatly affects its costs. In making this decision, the designer is faced with a complex issue. It is necessary to select the appropriate option from a wider set of available technologies, taking into account numerous influencing factors. In design practice, solving this problem is primarily based on the experience of designers and the recommendations of manufacturers of these technologies. In the academic literature, this problem has not been properly posed and solved, so there are no papers that comprehensively address this complex design problem. The main goal of this paper is to fill that gap. The presented approach consists of two basic stages. In the first stage, starting from the definition of the project task, potential technologies are generated and critical factors are considered, in order to arrive at a set of acceptable technologies. In the second stage, these technologies are ranked, and a basis for decision making is created. This stage is based on multi-criteria decision making: the Fuzzy Analytic Hierarchy Process (FAHP) method is used to determine the weights of the criteria, and the Weighted Aggregated Sum Product Assessment (WASPAS) method is used to obtain the rankings. The application of the defined approach is tested on real assignments (distribution warehouse, production warehouse, and holding warehouse) and is proven to be applicable to solving these types of problems. The results obtained for the three tested examples prove the suitability of the application of the proposed approach in terms of the aspects of both the quality of the solution and the speed of obtaining it. Considering the practical application of the suggested and filling the recognized literature gap, evident contributions are achieved.