We consider the low-energy effective action of string theory at order alpha', including R2 corrections to the Einstein-Hilbert gravitational action and nontrivial dilaton coupling. By means of a convenient field redefinition, we manage to express the theory in a frame that enables us to solve its field equations analytically and perturbatively in alpha' for a static spherically symmetric ansatz in an arbitrary number of dimensions. The set of solutions we obtain is compatible with asymptotically flat geometries exhibiting a regular event horizon at which the dilaton is well behaved. For the four-dimensional case, we also derive the stationary black hole configuration at first order in alpha' and in the slowly rotating approximation. This yields string theory modifications to the Kerr geometry, including terms of the form a, a2, alpha', and a alpha'. In addition, we obtain the first alpha' correction to the C metrics, which accommodates accelerating black holes. We work in the string frame and discuss the connection to the Einstein frame, for which rotating black holes have already been obtained in the literature.