Arches and Quintuplet are two young, massive clusters projected near the Galactic Centre. To date, studies focused on understanding their origin have been based on proper motions (PMs) derived in the clusters' reference frames and required some assumptions about their 3D motion. In this paper, we combine public PM catalogues of these clusters with the Gaia DR2 catalogue and, for the first time, transform the relative PMs of the Arches and Quintuplet clusters on to an absolute reference system. We find that the absolute PM of the Arches is (μαcos δ, μδ) = (−1.45 ± 0.23, −2.68 ± 0.14) mas yr−1 and that of the Quintuplet is (μαcos δ, μδ) = (−1.19 ± 0.09, −2.66 ± 0.18) mas yr−1. These values suggest that these systems are moving almost parallel to the Galactic plane. A measurement of the clusters' distances is still required to meaningfully constrain the clusters' orbits and shed light on the origin of the Arches and Quintuplet.