Low-carbon stabilization/solidification (S/S) is of increasing importance for sustainable treatment of hazardous wastes. In this study, we integrated carbon-negative rice husk biochar (RBC) and yard waste biochar (YBC) as green additives into the binder for S/S of municipal solid waste incineration (MSWI) fly ash. Experimental results illustrated that the addition of both biochars promoted cement hydration reaction via pozzolanic reaction and internal curing. In particular, the incorporation of 10 wt% RBC (rich in activated Si) significantly increased the content of C-S-H gel from 41.6 wt% (control sample) to 52.0 wt% and increased the average degree of connectivity of C-S-H gel from 1.43 to 1.52 as indicated by quantitative X-ray diffraction and ²⁹Si nuclear magnetic resonance analysis. The incorporation of RBC and YBC (20 or 30 wt%) enhanced the immobilization efficiency of potentially toxic elements in MSWI fly ash due to the additional hydration products and high adsorption ability of biochar. For instance, in R-80FA and Y-80FA samples (namely, 20 wt% binder dosage, of which RBC or YBC accounted for 10 wt% of binder), the immobilization efficiency for Pb could reach 96.2% and comply with the leachability limit. The biochar-modified S/S blocks achieved comparable strength to the cement-based S/S blocks, presenting a mechanically stable solidified matrix for engineering application. Therefore, this study expands the emerging application of biochar and demonstrates that biochar-augmented binder can ensure low-carbon and high-performance S/S of hazardous materials.