ABSTRACT In this paper, we combine the Early Science radio continuum data from the MeerKAT International GHz Tiered Extragalactic Exploration (MIGHTEE) Survey, with optical and near-infrared data and release the cross-matched catalogues. The radio data used in this work covers 0.86 deg2 of the COSMOS field, reaches a thermal noise of 1.7 μJy beam−1 and contains 6102 radio components. We visually inspect and cross-match the radio sample with optical and near-infrared data from the Hyper Suprime-Cam (HSC) and UltraVISTA surveys. This allows the properties of active galactic nuclei and star-forming populations of galaxies to be probed out to z ≈ 5. Additionally, we use the likelihood ratio method to automatically cross-match the radio and optical catalogues and compare this to the visually cross-matched catalogue. We find that 94 per cent of our radio source catalogue can be matched with this method, with a reliability of 95 per cent. We proceed to show that visual classification will still remain an essential process for the cross-matching of complex and extended radio sources. In the near future, the MIGHTEE survey will be expanded in area to cover a total of ∼20 deg2; thus the combination of automated and visual identification will be critical. We compare the redshift distribution of SFG and AGN to the SKADS and T-RECS simulations and find more AGN than predicted at z ∼ 1.