Hydrogels capable of responding to physicochemical dynamics in vivo are of significant interest in a variety of advanced biomedical applications. Herein, we develop novel fully biodegradable, biocompatible,highly elastomeric and pH-responsive copolymer hydrogels by direct crosslinking of the poly(glycerolsebacate) (PGS) pre-polymer and gelatin via their inherent functional groups without the use of any crosslinking agents. The addition of hydrophilic gelatin to the hydrophobic PGS enables the design of hydrogels with both elastomeric properties and water swelling capability as well as pH-responsive behaviours. The copolymer hydrogels were highly flexible and stretchable, enduring complex deformations such as stretching and knotting. Their Young’s moduli were in the range of 0.16–0.62 MPa, mimicking the values of some soft tissues. A three-dimensional tissue scaffold with interconnected pore structures was also fabricated which shows full shape recovery after compression, further demonstrating a high potential of these copolymers to be used in soft tissue engineering applications. The pH-responsive swelling ratios of the copolymer hydrogels were found to be up to 11-fold different in acidic and basic environments,which resulted in pH-dependent release profiles of a model drug. Moreover, a tunable biodegradation kinetics with an ultimate full degradation in 11 weeks in vitro and good cytocompatibility in the cell metabolicassay with mouse fibroblasts were also achieved with these copolymer hydrogels. The versatile multifunctionalities in these new copolymer hydrogels illustrate their great potential in soft tissue engineering and controlled drug delivery.