Source‐to‐sink dynamics are subjected to complex interactions between erosion, sediment transfer and deposition, particularly in an evolving tectonic and climatic setting. Here we use stratigraphic forward modelling (SFM) to predict the basin‐fill architecture of a multi‐source‐to‐sink system based on a state‐of‐the‐art numerical approach. The modelling processes consider key source‐to‐sink parameters such as water discharge, sediment load and grain size to simulate various sedimentary processes and transport mechanisms reflecting the dynamic interplay between erosion in the catchment area, subsidence, deposition and filling of the basin. The Cenozoic succession along the SW Barents Shelf margin provides a key area to examine controls on source‐to‐sink systems along a transform margin that developed during the opening of the North Atlantic when Greenland and Eurasian plates were separated (ca. 55 Ma onwards). Moreover, the gradual cooling which culminated in major glaciations in the northern hemisphere during the Quaternary (ca. 2.7 Ma), has affected the spatio‐temporal evolution of the sediment routing along the western Barents Shelf margin. This study aims to characterize the relative importance of different source areas within the source‐to‐sink framework through SFM. In the early Eocene, the SW Barents Shelf experienced a relatively equal sediment delivery from three principal source areas: (i) Greenland to the north, (ii) the Stappen High to the east, representing a local source terrain, and (iii) a major southern source (Fennoscandia). In the middle Eocene, our best‐fit modelling scenario suggests that the northern and the local eastern sources dominated over the southern source, collectively supplying large amounts of sand into the basin as evidenced by the submarine fans in Sørvestsnaget Basin. In the Oligocene (ca. 33 Ma) and Miocene (ca. 23 Ma), significant amounts of sediments were sourced from the east due to shelf‐wide uplift. Finally, this study highlights the dynamic nature and controls of sediment transfer in multi‐source‐to‐sink systems and demonstrates the potential of SFM to unravel tectonic and climatic signals in the stratigraphic record.