Bioprinting has emerged as an advanced method for fabricating complex 3D tissues. Despite the tremendous potential of 3D bioprinting, there are several drawbacks of current bioinks and printing methodologies that limit the ability to print elastic and highly vascularized tissues. In particular, fabrication of complex biomimetic structure that are entirely based on 3D bioprinting is still challenging primarily due to the lack of suitable bioinks with high printability, biocompatibility, biomimicry, and proper mechanical properties. To address these shortcomings, in this work the use of recombinant human tropoelastin as a highly biocompatible and elastic bioink for 3D printing of complex soft tissues is demonstrated. As proof of the concept, vascularized cardiac constructs are bioprinted and their functions are assessed in vitro and in vivo. The printed constructs demonstrate endothelium barrier function and spontaneous beating of cardiac muscle cells, which are important functions of cardiac tissue in vivo. Furthermore, the printed construct elicits minimal inflammatory responses, and is shown to be efficiently biodegraded in vivo when implanted subcutaneously in rats. Taken together, these results demonstrate the potential of the elastic bioink for printing 3D functional cardiac tissues, which can eventually be used for cardiac tissue replacement.