ABSTRACT We report the discovery of two new giant radio galaxies (GRGs) using the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) survey. Both GRGs were found within a ${∼}1\,$ deg2 region inside the COSMOS field. They have redshifts of z = 0.1656 and z = 0.3363 and physical sizes of 2.4 and 2.0 Mpc, respectively. Only the cores of these GRGs were clearly visible in previous high-resolution Very Large Array observations, since the diffuse emission of the lobes was resolved out. However, the excellent sensitivity and uv coverage of the new MeerKAT telescope allowed this diffuse emission to be detected. The GRGs occupy an unpopulated region of radio power – size parameter space. Based on a recent estimate of the GRG number density, the probability of finding two or more GRGs with such large sizes at z < 0.4 in a ${∼}1\,$ deg2 field is only 2.7 × 10−6, assuming Poisson statistics. This supports the hypothesis that the prevalence of GRGs has been significantly underestimated in the past due to limited sensitivity to low surface brightness emission. The two GRGs presented here may be the first of a new population to be revealed through surveys like MIGHTEE that provide exquisite sensitivity to diffuse, extended emission.