Our study aims to understand the variability of oceanic mesoscale eddies during contrasting (2009 and 2013) monsoon seasons and the role of such eddies on atmospheric deep convection over the Bay of Bengal (BoB). Oceanic eddies are detected and tracked using sea surface height anomalies (SSHA), by employing the Okubo-Weiss parameter eddy detection method. Significant differences in the SSHA and eddy activity are evident during the contrasting monsoon years. During the year 2013 (2009), anticyclonic eddies are predominant (absent) in the eastern BoB and longer (shorter) lifespans of cyclonic eddies are observed in the northern and western BoB. Analysis of time-longitude SSHA and zonal wind stress reveals the presence of strong (weak) equatorial downwelling Kelvin waves, coastal Kelvin waves and Rossby waves in the BoB during 2013 (2009) Indian summer monsoon (ISM). The variability of eddies in the BoB during contrasting monsoons is attributed by the remote forcing effect of planetary scale waves. Our study is extended to investigate the associated atmospheric deep convection over the regions of cyclonic and anticyclonic eddies. Lag-correlations demonstrates that SSHA leads the outgoing longwave radiation by four days over anticyclonic eddy regions. Findings from the present study provide new insight into the internal dynamics of the ocean.