Dynamical capture is a possible formation channel for binary black hole (BBH) mergers leading to highly eccentric merger dynamics and to gravitational wave (GW) signals that are morphologically different from those of quasicircular mergers. The future detection of these mergers by ground- or space-based GW interferometers can provide invaluable insights on astrophysical black holes, but it requires precise predictions and dedicated waveform models for the analysis. We present a state of the art effective-one-body (EOB) model for the multipolar merger-ringdown waveform from dynamical capture black hole mergers with arbitrary mass-ratio and nonprecessing spins. The model relies on analytical descriptions of the radiation reaction and waveform along generic orbits that are obtained by incorporating generic Newtonian prefactors in the expressions used in the quasicircular case. We demonstrate that the model reliably accounts for the rich phenomenology of dynamical captures, from direct plunge to successive close encounters up to merger. The parameter space is fully characterized in terms of the initial energy and angular momentum. Our model reproduces to a few percent the scattering angle from ten equal-mass, nonspinning, hyperbolic encounter numerical-relativity (NR) simulations. The agreement can be further improved by incorporating sixth post-Newtonian results in one of the EOB potentials while tuning currently unknown analytical parameters. Our results suggest that NR simulations of hyperbolic encounters (and dynamical captures) can be used to inform EOB waveform models for generic BBH mergers and encounters for present and future GW detectors.