Biochar has received attention due to its potential for mitigating climate change through carbon sequestration in soil and improving soil quality and crop productivity. This study evaluated the effects of rice straw biochar (RSB) and rice husk ash (RHA) each applied at 5 Mg ha−1 and four N levels (0, 40, 80, and 120 kg ha−1) on soil fertility, growth, and yield of rice and wheat for three consecutive rice–wheat rotations. RSB significantly increased electrical conductivity, dehydrogenase activity, and P and K contents when compared to control (no amendment) up to 7.5 cm soil depth. Both RSB and RHA did not influence shoot N concentration in wheat plant but significantly increased P and K concentrations at 60 days after sowing. Grain yields of both rice and wheat were significantly higher in RSB as compared to control (no amendment) and RHA treatments. While the highest grain yields of rice and wheat were observed at 120 kg N ha−1 in RHA and no biochar-treated plots, a significant increase in grain yields was observed at 80 kg N ha−1 in RSB treatment, thereby saving 40 kg N ha−1 in each crop. Both agronomic and recovery N efficiencies in rice and wheat were significantly higher in RSB-amended soil compared to control. Significant positive correlations were observed between soil N, P, and K concentrations and total N, P, and K concentrations in aboveground biomass of wheat at 60 days after sowing. This study showed the potential benefits of applying RSB for improving soil fertility and yields of rice and wheat in a rice–wheat system.