The electricity market clearing process can be affected to varying degrees by norms set by regulators. One possible rule is the Uniform Purchase Price, which is implemented, for example, in the Italian day-ahead market with the name of Prezzo Unico Nazionale, which literally means unique national price. This rule requires that all the consumers pay the same price in all the market zones. On the contrary, producers receive the zonal prices, which may differ from one zone to another. As a consequence, traditional market clearing techniques cannot be employed because of this difference in the paid and received price, and current state-of-the-art methods still rely on heuristic search procedures. Starting from a non-linear mixed integer bilevel formulation of the clearing process in presence of uniform purchase price, this paper shows how to obtain a mixed integer linear programming model, which is computationally tractable and able to solve exactly the uniform purchase price problem. Numerical results are reported by testing the algorithm using real data from the Italian day-ahead market.