Rapid gelation, low heat generation, biocompatibility, biodegradability, avoiding the use of a small molecular weight gelator and high gel fraction are the essential criteria for the successful biomedical application of an injectable hydrogel. We have developed a series of dually crosslinked injectable hydrogels of PEG and poly[2-(dimethylamino)ethyl methacrylate]-b-poly(N-isopropyl acrylamide) through extremely simple chemistry. The sequential nucleophilic substitution reaction between PEG containing reactive termini and the copolymer provided chemically crosslinked hydrogels with a gel fraction as high as 96-99\% with a gelation time of 1-4 min under physiological conditions. The gelation occurred with ca. 1 °C rise in temperature per gram of the injectable solution, avoids formation of by-products and can be performed in the temperature range of 20-37 °C. The hydrogels undergo hardening at a physiological temperature as confirmed by rheological experiments. The gelation time, water swelling, mechanical properties and degradability of the hydrogels depend on the PEG to copolymer ratio in the injectable solution. The rheological behaviour of the fully hydrated hydrogels showed desirable mechanical properties for soft tissue regeneration. The hydrogels exhibited blood compatibility and retained the viability of HepG2 cells with time. Platelet adhesion and aggregation followed by fibrinogen adsorption ability makes these hydrogels suitable for wound healing applications. © 2017 The Royal Society of Chemistry.