The magnetic properties of the two-dimensional, S = 1 honeycomb antiferromagnet BaNi₂V₂O₈ have been comprehensively studied using dc susceptibility measurements and inelastic neutron scattering techniques. The magnetic excitation spectrum is found to be dispersionless within experimental resolution between the honeycomb layers, while it disperses strongly within the honeycomb plane where it consists of two gapped spin-wave modes. The magnetic excitations are compared to linear spin-wave theory allowing the Hamiltonian to be determined. The first- and second-neighbor magnetic exchange interactions are antiferromagnetic and lie within the ranges 10.90meV ≤ J_n ≤ 13.35 meV and 0.85 meV ≤ J_nn ≤ 1.65 meV, respectively. The interplane coupling Jout is four orders of magnitude weaker than the intraplane interactions, confirming the highly two-dimensional magnetic behavior of this compound. The sizes of the energy gaps are used to extract the magnetic anisotropies and reveal substantial easy-plane anisotropy and a very weak in-plane easy-axis anisotropy. Together these results reveal that BaNi₂V₂O₈ is a candidate compound for the investigation of vortex excitations and Berezinsky-Kosterliz-Thouless phenomenon.