In this work, polycaprolactone–polyethylene glycol (PCL–PEG) based waterborne polyurethane–urea (WBPUU) inks have been developed for an extrusion-based 3D printing technology. The WBPUU, synthesized from an optimized ratio of hydrophobic polycaprolactone diol and hydrophilic polyethylene glycol (0.2:0.8) in the soft segment, is able to form a physical gel at low solid contents. WBPUU inks with different solid contents have been synthesized. The rheology of the prepared systems was studied and the WBPUUs were subsequently used in the printing of different pieces to demonstrate the relationship between their rheological properties and their printing viability, establishing an optimal window of compositions for the developed WBPUU based inks. The results showed that the increase in solid content results in more structured inks, presenting a higher storage modulus as well as lower tan δ values, allowing for the improvement of the ink’s shape fidelity. However, an increase in solid content also leads to an increase in the yield point and viscosity, leading to printability limitations. From among all printable systems, the WBPUU with a solid content of 32 wt% is proposed to be the more suitable ink for a successful printing performance, presenting both adequate printability and good shape fidelity, which leads to the realization of a recognizable and accurate 3D construct and an understanding of its relationship with rheological parameters.