We present first results on triazolium-based ionic liquids (ILs) as a novel class of nonderivatizing solvents for cellulose. Despite their chemical similarity to imidazolium cations, the 1,2,3-triazolium cation lacks the isolated ring proton, leading to reduced formation of N-heterocyclic carbenes (NHCs) and therefore to lower reactivity and less unwanted side reactions. We synthesized six ILs based on 1,2,3-triazolium and 1,2,4-triazolium cations. The acetates are room-temperature ionic liquids and dissolve a similar amount of cellulose as the corresponding imidazolium salt. From NMR spectroscopy of the solution, we rule out polymer degradation. The cellulose solubility rises with increasing anion basicity, while being almost independent of the cation. We perform molecular dynamics simulations and compute enthalpies of solvation, which quantitatively fit the experimental solubilities. Trajectory analysis reveals strong hydrogen bonds between acetate anions and cellulose hydroxyl groups, while the cations do not form strong hydrogen bonds with cellulose. Thus, the simulations provide an atomistic explanation of our experimental observations.