For an ordered subset of vertices in a connected graph , the metric representation of a vertex with respect to the set is the -vector , where represents the distance between the vertices and . The set is a metric generator for if every two different vertices of have distinct metric representations with respect to . A minimum metric generator is called a metric basis for and its cardinality, , the metric dimension of . It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae and tight bounds for the metric dimension of strong product graphs.