The Ocean is a highly dynamic source/sink of atmospheric trace gases which have a key role in climate. Emission estimates of these climate-relevant trace gases (CRTG) are still highly uncertain, partly because vast areas remain under-sampled. The Eastern Tropical Indian Ocean (ETIO) exemplifies such rather underexplored areas, in which assessments of distribution and air-sea fluxes of CRTGs have received comparatively less attention than their counterparts in the Atlantic and Pacific Oceans. Furthermore, large-scale observations across the region at comparable time scales are missing. In consequence, we still lack an understanding of the extent of zonal and meridional variability of dissolved CRTGs in the ETIO, their seasonal variability in response to synoptic meteorological events, and importantly, an estimate of the radiative balance for the region remains elusive. We present the results of high-resolution surface measurements of CO₂, CH₄, N₂O and CO which were conducted during three campaigns across the ETIO (to date, the most comprehensive survey in the region). Our observations reveal significant spatial and temporal variability in dissolved concentrations and sea-air fluxes of CRTGs, which was driven by the interplay between upwelling, riverine inputs and monsoonal influence. Using supplementary water column gas and turbulence observations, we present a mixed layer budget for each of them along the transition from the equatorial region to shelf waters of the Bay of Bengal, a known emission hotspot. An overall radiative balance for the region at the time of sampling suggests that N₂O and CH₄ emissions might offset up to one third of the CO₂ uptake, highlighting their non-negligible contribution to the net greenhouse gas (GHG) budget. These findings underscore the importance of including all major GHGs in future budgets of both open ocean and coastal waters.