<p>This paper deals with the study of the relationships between a class of bilevel programming problems and variational inequality problems, namely Minty and Stampacchia variational inequality problems, defined in terms of Clarke subdifferentials on Hadamard manifolds. We derive some existence results for the solutions of these variational inequality problems by employing the Knaster-Kuratowski-Mazurkiewicz (abbreviated as, KKM) lemma in the framework of Hadamard manifolds. Moreover, the derived results of this paper are employed to determine the optimal solution for the toll optimization problem with a single commodity (abbreviated as, TOPS). To demonstrate the validity and significance of the results established in this paper, we furnish nontrivial examples in the framework of well-known Hadamard manifolds, such as the Poincaré half-plane and the set of all real symmetric positive definite matrices, due to their practical applicability in medical image processing, machine learning, and data science. To the best of our knowledge, the equivalence relations between the solutions of bilevel programming problems and variational inequalities have not yet been studied in the framework of Hadamard manifolds.</p>