Summary: Value functions of impulse control problems are known to satisfy Quasi-Variational Inequalities (QVIs) [A. Bensoussan and J.-L. Lions, Methodes Mathematiques de l’Informatique, 11. Publie avec le concours du C.N.R.S. Paris: Dunod. XV, 596 p. (1982; Zbl 0491.93002)]. This paper proves the smooth-fit \(C^1\) property of the value function for multidimensional controlled diffusions, using a viscosity solution approach. We show by examples how to exploit this regularity property to derive explicitly an optimal policy and value functions.