Hydrogen sulfide (H2S) is a gasotransmitter molecule recognized for its role in cell signaling. Garlic-derived polysulfides including diallyl disulfide (DADS) and diallyl trisulfide (DATS) have been shown to release H2S. We investigated the mechanism of the reaction of DADS and DATS with biological thiols, including cysteine (Cys) and glutathione (GSH), using density functional theory. We propose that Cys and GSH react with DADS and DATS in their anionic forms. Thiol anions are much more likely to attack the sulfur atoms of DADS and DATS than the α-carbon of allyl groups. We found that nucleophilic attack of thiol anions on the peripheral sulfur of DATS is kinetically and thermodynamically more favorable than that on the central sulfur atom, resulting in the formation of allyl perthiol anion (ASS-). In the presence of Cys or GSH, H2S is released by proton-shuffle from the thiol to ASS-, followed by another nucleophilic attack by thiol anion on ASSH. Our computed potential energy surfaces revealed that GSH and Cys are capable of releasing H2S from DATS and that DADS is a much poorer H2S donor than DATS.