We present the MARD-Y3 catalogue of between 1086 and 2171 galaxy clusters (52percent and 65percent new) produced using multicomponent matched filter (MCMF) follow-up in 5000deg2 of DES-Y3 optical data of the 20000 overlapping ROSAT All-Sky Survey source catalogue (2RXS) X-ray sources. Optical counterparts are identified as peaks in galaxy richness as a function of redshift along the line of sight towards each 2RXS source within a search region informed by an X-ray prior. All peaks are assigned a probability fcont of being a random superposition. The clusters lie at 0.02 > z > 1.1 with more than 100 clusters at z < 0.5. Residual contamination is 2.6percent and 9.6percent for the cuts adopted here. For each cluster we present the optical centre, redshift, rest frame X-ray luminosity, M500 mass, coincidence with NWAY infrared sources, and estimators of dynamical state. About 2percent of MARD-Y3 clusters have multiple possible counterparts, the photo-zs are high quality with z/(1 + z)= 0.0046, and 1percent of clusters exhibit evidence of X-ray luminosity boosting from emission by cluster active galactic nuclei. Comparison with other catalogues (MCXC, RM, SPT-SZ, Planck) is performed to test consistency of richness, luminosity, and mass estimates. We measure the MARD-Y3 X-ray luminosity function and compare it to the expectation from a fiducial cosmology and externally calibrated luminosity- and richnessmass relations. Agreement is good, providing evidence that MARD-Y3 has low contamination and can be understood as a simple two step selection X-ray and then optical of an underlying cluster population described by the halo mass function.