Phytoplankton biomass, quantified as the concentration of chlorophyll-a (CHL), is the base of the marine food web that supports fisheries production in the Bay of Bengal (BoB). Nutrients from river discharge, the ocean subsurface layer, and the atmosphere have been reported to determine CHL in the BoB. Which source of nutrients mainly determines CHL in different parts of the bay has not been determined. Furthermore, how climate variations influence nutrient inputs from different sources and their impacts on CHL have not been detailed. To address these questions, we used relationships between satellite-derived CHL and in situ river discharge data (a proxy for river-borne nutrients) from 1997 to 2016, physical variables, and modeled dust deposition (DD), a proxy for atmosphere-borne nutrients. Nutrients supplied from the ocean subsurface layer were assessed based on variations in physical parameters (i.e., wind stress curl, sea surface height anomaly, and sea surface temperature). We found that nutrients from the Ganges and Brahmaputra Rivers were important for CHL along the northern coast of the bay. By increasing rainfall and river discharge, La Niña extended high-CHL waters further southward. Nutrients from the ocean subsurface layer determine CHL variations mainly in the southwestern bay. We suggest that the variations in the supply of nutrients from the subsurface layer are related to the generation of mesoscale cyclonic eddies during La Niña, a negative Indian Ocean Dipole, or both. Climate-driven cyclonic eddies together with cyclones can intensify Ekman divergence and synergistically lead to a pronounced increase in CHL in the southwestern bay. Nutrients from the atmosphere mainly determine CHL in the central/eastern BoB. We further suggest that DD in the central/eastern BoB is influenced by ENSO with a 6–7-month time lag. CHL in the central/eastern bay responds to the ENSO 6–7 months after the ENSO peak because of the 6–7-month lag between ENSO and DD. This report provides valuable information needed to plan necessary actions for climate adaptation in local fisheries activities by elucidating how climate variations influence phytoplankton.