  The goal of this article is to study minimal surfaces in $\mathbb{M}^2 \times
\mathbb{R}$ having finite total curvature, where $\mathbb{M}^2$ is a Hadamard
manifold. The main result gives a formula to compute the total curvature in
terms of topological, geometrical and conformal data of the minimal surface. In
particular, we prove the total curvature is an integral multiple of $2\pi$.
