Mining high utility itemsets is a keystone in several data analysis tasks. High Utility Itemset Mining generalizes the frequent itemset mining problem by considering item quantities and weights. A high utility itemset is a set of items that appears in the transadatabase and having a high importance to the user, measured by a utility function. The utility of a pattern can be quantified in terms of various objective criteria, e.g., profit, frequency, and weight. Constraint Programming (CP) and Propositional Satisfiability (SAT) based frameworks for modeling and solving pattern mining tasks have gained a considerable attention in recent few years. This paper introduces the first declarative framework for mining high utility itemsets from transaction databases. First, we model the problem of mining high utility itemsets from transaction databases as a propositional satifiability problem. Moreover, to facilitate the mining task, we add an additional constraint to the efficiency of our method by using weighted clique cover problem. Then, we exploit the efficient SAT solving techniques to output all the high utility itemsets in the data that satisfy a user-specified minimum support and minimum utility values. Experimental evaluations on real and synthetic datasets show that the performance of our proposed approach is close to that of the optimal case of state-of-the-art HUIM algorithms.