Recent observational studies provided preliminary insights on the interannual variability of Bay of Bengal (BoB) Sea Surface Salinity (SSS), but are limited by the poor data coverage. Here, we describe the BoB interannual SSS variability and its driving processes from a regional eddy-permitting ocean general circulation model forced by interannually varying air-sea fluxes and altimeter-derived discharges of major rivers over the past two decades. Simulated interannual SSS variations compare favorably with both in situ and satellite data and are largest in boreal fall in three regions: the northern BoB, the coastal region off east India, and the Andaman Sea. In the northern BoB, these variations are independent from those in other regions and mostly driven by summer-fall Ganga-Brahmaputra runoff interannual variations. In fall, remote forcing from the Indian Ocean Dipole results in anticlockwise anomalous horizontal currents that drive interannual SSS variations of opposite polarity along the east coast of India and in the Southern Andaman Sea. From winter onward, these anomalies are damped by vertical mixing in the northern BoB and along the east coast of India and by horizontal advection in the Southern Andaman Sea. While river runoff fluctuations locally play a strong role near the Ganga-Brahmaputra river mouth, wind-driven interannual current anomalies are responsible for a large fraction of SSS interannual variability in most of the basin.