Cloud Computing (CC) has become increasingly popular since it provides a wide variety of customized and reliable computational services. With the rapid growth of this technology, more and more IT services providers compete to offer high-quality and cost-effective cloud services that best fulfill their customers' needs. Given the vast diversity of these offers, the choice of the most appropriate Cloud Service Provider (CSP) became a dilemma that confuses most cloud customers. Many diverged criteria have to be considered to precisely evaluate services offered by several CSPs, some of these criteria cannot be quantified easily such as usability and security. The selection of the best CSP is thus a complex Multi-Criteria Decision Making (MCDM) problem that needs to be addressed efficiently. Previous studies of this problem employed MCDM methods that are either unfeasible when it is difficult or meaningless to quantify alternatives over criteria or computationally expensive and inconsistent when relative preferences of alternatives and criteria are used instead. In this paper, we propose a novel MCDM approach that is feasible, efficient and consistent using relative preferences of criteria and alternatives. The proposed approach incorporates Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and the Best Worst Method (BWM) to rank CSPs using evaluation criteria characterizing their services. The integrated approach has been tested and validated through a use-case scenario which demonstrates its effectiveness and correctness. We have also compared the proposed approach to the most commonly used MCDM approach, Analytical Hierarchical Process (AHP). The results clearly show that the proposed approach outperforms AHP in terms of computational complexity and consistency; hence, it is more efficient and reliable than AHP. INDEX TERMS Cloud computing (CC), cloud service providers (CSPs), multiple-criteria decision-making (MCDM), best worst method (BWM), technique for order of preference by similarity to ideal solution (TOPSIS), analytical hierarchical process (AHP).