Wetlands are important sources of methane (CH4) and sinks of carbon dioxide (CO2). However, little is known about CH4 and CO2 fluxes and dynamics of seasonally flooded tropical forests of South America in relation to local carbon (C) balances and atmospheric exchange. We measured net ecosystem fluxes of CH4 and CO2 in the Pantanal over 2014–2017 using tower‐based eddy covariance along with C measurements in soil, biomass and water. Our data indicate that seasonally flooded tropical forests are potentially large sinks for CO2 but strong sources of CH4, particularly during inundation when reducing conditions in soils increase CH4 production and limit CO2 release. During inundation when soils were anaerobic, the flooded forest emitted 0.11 ± 0.002 g CH4‐C m−2 d−1 and absorbed 1.6 ± 0.2 g CO2‐C m−2 d−1 (mean ± 95% confidence interval for the entire study period). Following the recession of floodwaters, soils rapidly became aerobic and CH4 emissions decreased significantly (0.002 ± 0.001 g CH4‐C m−2 d−1) but remained a net source, while the net CO2 flux flipped from being a net sink during anaerobic periods to acting as a source during aerobic periods. CH4 fluxes were 50 times higher in the wet season; DOC was a minor component in the net ecosystem carbon balance. Daily fluxes of CO2 and CH4 were similar in all years for each season, but annual net fluxes varied primarily in relation to flood duration. While the ecosystem was a net C sink on an annual basis (absorbing 218 g C m−2 (as CH4‐C + CO2‐C) in anaerobic phases and emitting 76 g C m−2 in aerobic phases), high CH4 effluxes during the anaerobic flooded phase and modest CH4 effluxes during the aerobic phase indicate that seasonally flooded tropical forests can be a net source of radiative forcings on an annual basis, thus acting as an amplifying feedback on global warming.