We study the strongly anisotropic quasi-one-dimensional S = 1 quantum magnet NiCl₂⋅4SC(NH₂)₂ using elastic and inelastic neutron scattering. We demonstrate that a magnetic field splits the excited doublet state and drives the lower doublet state to zero energy at a critical field H_c1. For H_c1 < H < H_c2, where H_c2 indicates the transition to a fully magnetized state, three-dimensional magnetic order is established with the AF moment perpendicular to the magnetic field. We mapped the temperature/magnetic field phase diagram, and we find that the total ordered magnetic moment reaches m_tot = 2.1 μ_B at the field μ₀H = 6 T and is thus close to the saturation value of the fully ordered moment. We study the magnetic spin dynamics in the fully magnetized state for H > H_c2, and we demonstrate the presence of an AF interaction between Ni²⁺ on the two interpenetrating sublattices. In the antiferromagnetically ordered phase, the spin-waves that develop from the lower-energy doublet are split into two modes. This is most likely the result of the presence of the AF interaction between the interpenetrating lattices.