We present the results of photometric, astrometric, and spectroscopic follow-up of L dwarf candidates identified in the Hyades cluster by Hogan et al. We obtained low-resolution optical spectroscopy with the Optical System for Imaging and low-intermediate Resolution Integrated Spectroscopy spectrograph on the Gran Telescopio de Canarias for all 12 L dwarf candidates as well as new J-band imaging for a subsample of 8 to confirm their proper motion. We also present mid-infrared photometry from the Wide Field Infrared Survey Explorer for the Hyades L and T dwarf candidates and estimate their spectroscopic distances, effective temperatures, and masses. We confirm the cool nature of several L dwarf candidates and confirm astrometrically their membership, bridging the gap between the coolest M dwarfs and the two T dwarfs previously reported in the Hyades cluster. These members represent valuable spectral templates at an age of 625 Myr and slightly supersolar metallicity (Fe/H = +0.13). We update the Hyades mass function across the hydrogen-burning limit and in the substellar regime. We confirm a small number numbers of very low mass members below ∼ 0.1 M☉ belonging to the Hyades cluster.