Oceanic Rossby waves can propagate climate signals over considerable distances over long timescales. Using a long simulation from a coupled climate model, we examine oceanic and mixed atmosphere‐ocean teleconnections to the south‐western Indian Ocean (SWIO) associated with Rossby waves excited by the El Niño‐Southern Oscillation (ENSO). Reconstruction of propagating ENSO‐induced sea‐level anomalies from the simulation using an optimized linear wave model with dissipation highlights the prominent role of baroclinic, rather than barotropic, Rossby waves in modulating sea‐surface heights. Between 9.5° and 18.5°S, El Niño‐associated anomalous anticyclonic wind‐stress fields initiate downwelling Rossby waves, potentially influencing SWIO regional climate around 1–4 seasons after El Niño peak, while also destructively interfering with upwelling waves triggered on the eastern boundary by oceanic teleconnections. Further south, weaker ENSO winds, dissipation, non‐linear processes, and interference from higher‐mode Rossby waves limit ENSO influences in the SWIO. In the model, ENSO‐associated predictability is therefore constrained by the “atmospheric” rather than “oceanic” bridge.