Strategies to encapsulate cells in cytocompatible three-dimensional hydrogels with tunable mechanical properties and degradability without harmful gelling conditions are highly desired for regenerative medicine applications. Here we reported a method for preparing poly(ethylene glycol)-co-polycarbonate hydrogels through copper-free, strain-promoted azide–alkyne cycloaddition (SPAAC) click chemistry. Hydrogels with varying mechanical properties were formed by “clicking” azido-functionalized poly(ethylene glycol)-co-polycarbonate macromers with dibenzocyclooctyne-functionalized poly(ethylene glycol) under physiological conditions within minutes. Bone marrow stromal cells encapsulated in these gels exhibited higher cellular viability than those encapsulated in photo-cross-linked poly(ethylene glycol) dimethacrylate. The precise control over the macromer compositions, cytocompatible SPAAC cross-linking, and the degradability of the polycarbonate segments make these hydrogels promising candidates for scaffold and stem cell assisted tissue repair and regeneration.