Abstract: This invention is related to technology of tissue-engineered constructs biofabrication from tissue spheroids. This novel technology of scaffold-free, nozzle-free and label-free bioassembly opens a unique opportunity for rapid biofabrication of 3D tissue and organ constructs with complex geometry. A combination of intense magnetic and acoustic fields could enable rapid levitational bioassembly of complex-shaped 3D tissue constructs from tissue spheroids at low concentration of paramagnetic agent (gadolinium salt) in the medium. Magnetic field provides objects levitation due to field configuration with the lowest magnetic field density in the center of working volume of medium with tissue spheroids, and three-dimensional acoustic field forms internal and external construct geometry by means of acoustic radiation forces.