The masses and decay widths of charmonium states are studied in the presence of strong magnetic fields. The mixing between the pseudoscalar and vector charmonium states at rest is observed to lead to appreciable negative (positive) shifts in the masses of the pseudoscalar (longitudinal component of the vector) charmonium states in vacuum/hadronic medium in the presence of high magnetic fields. The pseudoscalar and vector charmonium masses in the hadronic medium, calculated in an effective chiral model from the medium changes of a scalar dilaton field, have additional significant modifications due to the mixing effects. The masses of the $D$ and $bar D$ mesons in the magnetized hadronic matter are calculated within the chiral effective model. The partial decay widths of the vector charmonium state to $Dbar D$ are computed using a field theoretical model for composite hadrons with quark/antiquark constituents, and are compared to the decay widths calculated using an effective hadronic Lagrangian. The effects of the mixing are observed to lead to significant contributions to the masses of the pseusoscalar and vector charmonium states, and an appreciable increase in the decay width $psi(3770) rightarrow Dbar D$ at large values of the magnetic fields. These studies of the charmonium states in strong magnetic fields should have observable consequences on the dilepton spectra, as well as on the production of the open charm mesons and the charmonium states in ultra relativistic heavy ion collision experiments.
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