Abstract Despite recent advances in extrusion bioprinting of cell‐laden hydrogels, using naturally derived bioinks to biofabricate complex elastic tissues with both satisfying biological functionalities and superior mechanical properties is hitherto an unmet challenge. Here, we address this challenge with precisely designed biological tough hydrogel bioinks featuring a double‐network structure. The tough hydrogels consisted of energy‐dissipative dynamically crosslinked glycosaminoglycan hyaluronic acid (o‐nitrobenzyl‐grafted hyaluronic acid) and elastin through Schiff's base reaction, and free‐radically polymerized gelatin methacryloyl. The incorporation of elastin further improved the elasticity, stretchability (∼170% strain), and toughness (∼45 kJ m−3) of the hydrogels due to the random coiling structure. We used this novel class of hydrogel bioinks to bioprint several complex elastic tissues with good shape retention. Furthermore, in vitro and in vivo experiments also demonstrated that the existence of elastin in the biocompatible bioinks facilitated improved cell behaviors and biological functions of bioprinted tissues, such as cell spreading and phenotype maintenance as well as tissue regeneration. The results confirmed the potential of the elastin‐containing tough hydrogel bioinks for bioprinting of 3D complex elastic tissues with biological functionalities, which may find widespread applications in elastic tissue regeneration.