Gravitational wave astronomy might allow us to detect the coalescence of low-brightness astrophysical compact objects which are extremely difficult to be observed with current electromagnetic telescopes. Besides classical sources like black holes and neutron stars, other candidates include exotic compact objects (ECOs), which could exist in theory but have never yet been observed in nature. Among different possibilities, here we consider dark stars, astrophysical compact objects made of dark matter such that only interact with other stars through gravity. We study numerically the dynamics and the gravitational waves produced during the binary coalescence of equal mass dark stars composed by bosonic fields. These results are compared both with Post-Newtonian approximations and with previous simulations of binary boson stars, which interact both through gravity and matter. Our analysis indicates that dark boson stars belong to a new kind of compact objects, representing stars made with different species, whose merger produces a gravitational signature clearly distinguishable from other astrophysical objects like black holes, neutron stars and even boson stars.