We present an algorithm for classifying the nearby transient objects detected by the Gaia satellite. The algorithm will use the low-resolution spectra from the blue and red spectro-photometers on board of the satellite. Taking a Bayesian approach we model the spectra using the newly constructed reference spectral library and literature-driven priors. We find that for magnitudes brighter than 19 in Gaia $G$ magnitude, around 75\% of the transients will be robustly classified. The efficiency of the algorithm for SNe type I is higher than 80\% for magnitudes $G≤$18, dropping to approximately 60\% at magnitude $G$=19. For SNe type II, the efficiency varies from 75 to 60\% for $G≤$18, falling to 50\% at $G$=19. The purity of our classifier is around 95\% for SNe type I for all magnitudes. For SNe type II it is over 90\% for objects with $G ≤$19. GS-TEC also estimates the redshifts with errors of $σ_z \le$ 0.01 and epochs with uncertainties $σ_t ≃$ 13 and 32 days for type SNe I and SNe II respectively. GS-TEC has been designed to be used on partially calibrated Gaia data. However, the concept could be extended to other kinds of low resolution spectra classification for ongoing surveys. ; Comment: 17 pages, 14 figures, accepted to be published in Monthly Notices of the Royal Astronomical Society [MNRAS]