We present deep Swift follow-up observations of a sample of 94 unidentified X-ray sources from the XMM-Newton Slew Survey. The X-ray Telescope (XRT) on-board Swift detected 29 per cent of the sample sources; the flux limits for undetected sources suggest the bulk of the Slew Survey sources are drawn from one or more transient populations. We report revised X-ray positions for the XRT-detected sources, with typical uncertainties of 2.9 arcsec, reducing the number of catalogued optical matches to just a single source in most cases. We characterize the sources detected by Swift through their X-ray spectra and variability and via Ultraviolet-Optical Telescope photometry and using catalogued near-infrared, optical and radio observations of potential counterparts. Six sources can be associated with known objects and eight sources may be associated with unidentified ROSAT sources within the 3{sigma} error radii of our revised X-ray positions.