Context. Ellerman bombs (EBs) are observational signatures of small-scale magnetic reconnection, key to understanding the lower solar atmosphere. While their role in active regions has been widely studied using the Hα line, near-ultraviolet (NUV) spectra routinely observed by the Interface Region Imaging Spectrograph (IRIS) offer a promising alternative for EB identification, enabling large-scale studies. Aims. We aim to identify the most important spectral signatures of EBs in the IRIS NUV spectra. With this, we seek to develop a robust criterion for their detection solely using the IRIS NUV spectra. In parallel, we determine the typical atmospheric stratification associated with EBs. Methods. We used four coordinated observations between the Swedish 1-m Solar Telescope (SST) and IRIS. Using the Hα line as a reference, we detected 18 different EBs and studied their associated IRIS NUV spectra. In addition, we used the IRIS2+ inversion tool to infer the temperature, line-of-sight velocity, and nonthermal broadening from the EB spectra. Results. The defining feature of EBs in the IRIS NUV is the enhancement of the wings of the subordinated Mg II triplet between the Mg II h&k lines. Inversions reveal that these signatures are produced by a localized temperature increase of ∆T ~ 1670 K around log(τ) = -3.8. Using only the Mg II triplet signatures, we found a detection criterion that successfully recovered 14 of 18 Hα-detected EBs. In addition, the shape of the Mg II h&k lines in relation to the Mg II triplet can serve as a proxy for the EB formation height. Conclusions. The NUV spectrum observed by IRIS is a good candidate for detecting EBs, opening the doors to large-scale studies across the extensive IRIS database, removing the dependence on Hα observations. This capability bridges the gap between small- and large-scale event studies, which was not possible before due to the lack of coordinated observations.