We derive bounds on the Dirac Yukawa couplings of the neutrinos in seesaw models using the recent Large Hadron Collider (LHC) data on Higgs decays for the case where the Standard Model singlet heavy leptons needed for the seesaw mechanism have masses in the 100 GeV range. Such scenarios with large Yukawa couplings are natural in Inverse Seesaw models since the small neutrino mass owes its origin to a small Majorana mass of a new set of singlet fermions. Large Yukawas with sub-TeV mass right-handed neutrinos are also possible for certain textures in Type-I seesaw models, so that the above bounds also apply to them. We find that the current Higgs data from the LHC can put bounds on both electron- and muon-type Yukawa couplings of order 10^{-2}. ; Comment: 24 pages, 3 figures, 8 tables; version accepted for publication in PRD