We give a sharp estimate of the modulus of continuity of the solution to the Dirichlet problem for the complex Hessian equation of order [Formula: see text], [Formula: see text], with a continuous right-hand side and a continuous boundary data in a bounded strongly [Formula: see text]-pseudoconvex domain [Formula: see text]. Moreover, when the right-hand side is in [Formula: see text] for some [Formula: see text], and the boundary value function is [Formula: see text]-smooth we prove that the solution is Hölder continuous.