Modern ultrasound (US) imaging is increasing its clinical impact, particularly with the introduction of US-based quantitative imaging biomarkers. Continued development and validation of such novel imaging approaches requires imaging phantoms that recapitulate the underlying anatomy and pathology of interest. However, current US phantom designs are generally too simplistic to emulate the structure and variability of the human body. Therefore, there is a need to create a platform that is capable of generating well-characterized phantoms that can mimic the basic anatomical, functional, and mechanical properties of native tissues and pathologies. Using a 3D-printing technique based on stereolithography, we fabricated US phantoms using soft materials in a single fabrication session, without the need for material casting or back-filling. With this technique, we induced variable levels of stable US backscatter in our printed materials in anatomically relevant 3D patterns. Additionally, we controlled phantom stiffness from 7 to >120 kPa at the voxel level to generate isotropic and anisotropic phantoms for elasticity imaging. Lastly, we demonstrated the fabrication of channels with diameters as small as 60 micrometers and with complex geometry (e.g., tortuosity) capable of supporting blood-mimicking fluid flow. Collectively, these results show that projection-based stereolithography allows for customizable fabrication of complex US phantoms.