Large impact basins are present on many of the icy satellites of the outer solar system. Assuming that their present-day topography is uncompensated, such basins can cause significant poleward reorientations for slow-rotating satellites. This reorientation may have been accompanied by transient large-amplitude wobble. The largest basins on Tethys, Rhea and Titania are predicted to have caused reorientations of roughly 4°, 7° and 12°, respectively, resulting in global tectonic stresses up to ∼0.5 MPa. The potential anomalies associated with the basins can be up to one-third of those expected for a hydrostatic, tidally- and rotationally-deformed body, and may complicate interpretation of the satellite interior structure. Pluto and Charon, because of their slow rotation, are also likely to have undergone reorientation of 10–20° if they possess impact basins of comparable sizes to those of the Saturnian satellites.