Hydrogel-based localised drug delivery minimises systemic side effects and a linear release profile ensuring a sustained drug release over time, crucial for long-term therapy. The current paper describes the use of the Copper(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAc) to append azidified Dexamethasone (Dex) onto dendrons of first- and second-generation PEGs. Crosslinking with thiolated PEGs using either thiol-acrylate or nucleophilic addition reactions yielded gels containing β-thio-ether ester groups that imparted enhanced hydrolytic susceptibility. In vitro gel degradation was followed gravimetrically and expressed as swelling ratios. Thiol-acrylate crosslinked hydrogels exhibited zero-order Dex release kinetics over 11, 27, and 16 days (G1, G1-star, and G2). Crosslinking the G1-gels by nucleophilic addition also resulted in linear release and the end point was reached in 5 days. Hydrolysis was accounted as the main release mechanism for covalently bound Dex, while physically incorporated Dex showed undefined rapid burst or first-order release, with most of the drug released in the initial 1–3 days. Eluates from covalently bound Dex maintained high activity, whereas Trap-Dex gels lost activity over time, as detected by the upregulation of luciferase expression from a transformed cell line. This novel chemistry combination offers precise drug release control applicable beyond Dex to drugs with suitable nucleophilic groups.