Alginate is a common component of bioinks due to its well-described ionic crosslinking mechanism and tunable viscoelastic properties. Extrusion-based 3D-printing of alginate inks requires additives, such as gelatin and Pluronic, pre- or post-printing crosslinking processes and/or coextrusion with crosslinkers. In this work, we aim to develop a different printing approach for alginate-based inks, introducing 3D-reactive printing. Indeed, the control over the crosslinking kinetics and the printing time allowed printing different inks while maintaining their final composition unaltered to identify a suitable formulation in terms of printability. Alginate solutions were crosslinked with insoluble calcium salts (CaCO3) inducing a dynamic modification of their microstructure and viscoelastic properties over time. The monitoring of fiber printability and internal microstructure, at different time points of ink gelation, was performed by means of a well-defined set of rheological tests to obtain a priori ink properties for the a posteriori 3D-printing process. This new perspective allowed 3D-reactive printing of alginate fibers with predetermined properties, without involving post-extrusion crosslinking steps and additives.