Biochar application is considered a potential approach to mitigating greenhouse gas emissions (GHGs) from the agricultural sector and improving soil physicochemical properties. Thus, we conducted a field experiment to examine the efficacy of biochar application rates in combination with water management practices on soil methane (CH4) and nitrous oxide (N2O) emissions and carbon increment in the Vietnamese Mekong Delta (VMD). Rice husk biochar (RB) and Melaleuca biochar (MB) were incorporated in the topsoil (0–20 cm) at 5 and 10 Mg ha−1, followed by the water management regimes of continuous flooding (CF) and an alternative wetting and drying (AWD). The results identified that biochar application rates and water management measures were major factors in decreasing CH4 and N2O emissions. Compared with the conventional practice, the RB and MB amendment in the rice fields under CF practices reduced 12.9–21.3% of total GHGs (tGHGs), while biochar incorporation under the AWD management practice reduced from 22.3% to 30.5% tGHGs. Compared to CF treatments, biochar amendment concerning the AWD regime lowered from 25.4% to 31.6% tGHGs. Increasing biochar from 5 to 10 Mg ha−1 did not reduce tGHGs considerably. We identified that biochar application significantly increased grain yields from 12.8% to 20.6% under the CF management practice, while the percentage varied from 2.5% to 3.8% for the AWD practice. Similarly, higher grain yields were achieved from 4.9% to 13.7% by applying AWD compared to the CF treatments. Our findings showed that although higher biochar application rates could reduce the tGHGs, the difference in biochar types and water management applications in connection with the tGHGs was neglectable. Incorporating biochar enhanced soil bulk density and porosity under AWD and CF practices. Going forward in further studies, we recommend a long-term biochar application in the VMD’s low-lying paddy fields with a broader range of biochar rates under different soil types.