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 on-board Swift detected 29% of the sample sources; the flux limits for undetected sources suggests 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, reducing the number of catalogued optical matches to just a single source in most cases. We characterise the sources detected by Swift through their X-ray spectra and variability and via UVOT photometry and catalogued nIR, optical and radio observations. Six sources can be associated with known objects and 8 may be associated with unidentified ROSAT sources within the 3-sigma error radii of our revised X-ray positions. We find 10 of the 30 XRT-detected sources are clearly stellar in nature, including one periodic variable star and 2 high proper motion stars. For 11 sources we propose an AGN classification, among which 4 are detected with BAT and 3 have redshifts spanning z = 0.2 - 0.9 obtained from the literature or from optical spectroscopy presented here. The 67 Slew Survey sources we do not detect with Swift are studied via their characteristics in the Slew Survey and by comparison with the XRT and BAT detected population. We suggest that these are mostly if not all extragalactic, though unlikely to be highly absorbed sources in the X-rays such as Compton thick AGN. A large number of these are highly variable soft X-ray sources. A small fraction of mainly hard-band detections may be spurious. This follow-up programme brings us a step further to completing the identifications of a substantial sample of XMM-Newton Slew Survey sources, important for understanding the nature of the transient sky and allowing flux-limited samples to be constructed.
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