We present a study of the detectability of transient events associated with galaxies for the Gaia European Space Agency astrometric mission. We simulated the on-board detections, and on-ground processing for a mock galaxy catalogue to establish the properties required for the discovery of transient events by Gaia, specifically tidal disruption events (TDEs) and supernovae (SNe). Transients may either be discovered by the on-board detection of a new source or by the brightening of a previously known source. We show that Gaia transients can be identified as new detections on-board for offsets from the host galaxy nucleus of 0.1-0.5 arcsec, depending on magnitude and scanning angle. The Gaia detection system shows no significant loss of SNe at close radial distances to the nucleus. We used the detection efficiencies to predict the number of transients events discovered by Gaia. For a limiting magnitude of 19, we expect around 1300 SNe per year: 65 per cent SN Ia, 28 per cent SN II and 7 per cent SN Ibc, and ~20 TDEs per year.