We generate self-assembled biocompatible scaffolds with excellent structural integrity based on complex-forming block polyelectrolytes that enable extrusion-based 3D bioprinting of large constructs from low-viscosity bioinks. Despite remarkable progress of biofabrication techniques in tissue engineering, the development of extrudable bioinks that perform optimally at physiological temperatures remains a major challenge. Most biopolymer and photocurable precursor solutions exhibit low viscosities at 37 °C, resulting in undesirable flows and loss of form prior to chemical crosslinking. Temperature-sensitive bioinks, such as gelatin methacryloyl (GelMA), can be deposited near their gelling point, but suffer from suboptimal temperature-induced pre-gelation, poor cell viability emerging from long holding times in the cooled cartridges, inefficient temperature transfer from the print bed, and discontinuous layer-by-layer fabrication. Here, we demonstrate that block polyelectrolyte additives serve as effective viscosity enhancers when added to non-extrudable precursor solutions. Rapid, electrostatic self-assembly of block polyelectrolytes into either jammed micelles or interconnected networks provides hydrogel scaffoldings that form nearly instantly, lend initial structural robustness upon deposition, and enhance shear and tensile strength of the cured bioinks. Moreover, our approach enables continuous extrusion without the need of chemical crosslinking between individual layers, paving the way for fast biomanufacturing of human-scale tissue constructs with improved inter-layer bonding.