The variability of Quaternary landforms preserved in the Tabernas basin of southeast (SE) Spain raises numerous questions concerning the roles of external forcing mechanisms (e.g. tectonics and/or climate) and internal landscape properties (e.g. lithological controls) in the evolution of the basin‐wide fluvial system over Late Quaternary timescales. In this study, we apply the FLUVER2 numerical model to investigate the significance of these landscape controls upon patterns of landscape evolution. We highlight the complications of generating realistic input datasets for use in the modelling of long‐term landscape evolution (e.g. discharge and runoff datasets). Model outputs are compared to extensive field mapping of fluvial terraces, their sedimentary architecture and optically stimulated luminescence dating results of the terraces. The results demonstrate the significance of non‐linear rates of flexural tectonic uplift towards the west of the Tabernas Basin which have controlled base levels throughout the Quaternary and promoted the formation of a series of diverging fluvial terraces. Our numerical model results further highlight the importance of climate cycles upon river terrace formation. Basin‐wide aggradation events were modelled during the transition from Marine Isotope Stage (MIS) 6 to 5 and the Last Glacial Maximum (LGM) as supported by field evidence. This aggradational pattern supports the regional hypothesis of terrace formation during global glacial cycles and cold‐to‐warm stage transitions and supports the use of sea surface temperature climate proxy data in the modelling exercise. The availability of sediments derived from the surrounding hillslopes and adjacent alluvial fans explains the generation of substantial terrace aggradations.