Applying additive manufacturing technology to the principles of fibre reinforcement of hydrogels, we have fashioned weak hydrogels into mechanically enhanced composites. We combined the extracellular matrix-like structure of gelatin-methacrylamide (GelMA) and GelMA/hyaluronic acid-methacrylamide (HAMA) hydrogels with highly oriented poly(ε-caprolactone) (PCL) fibres fabricated by Melt Electrospinning Writing (MEW) to achieve fibre-reinforced GelMA/HAMA composites with improved compressive properties. Stacked fibres with lay-down patterns of 0°-90° and 0°-60°-120°, and spacing of 400 and 800 μm were prepared by MEW. These defined fibrous structures were infiltrated with hydrogels, namely GelMA (10%) and GelMA/HAMA (0.125%, 0.25% and 0.5%) in custom-made moulds and crosslinked by a reduction-oxidation initiating system (ammonium persulphate/tetramethylethylenediamine). Mechanical properties and deformation characteristics of the constructs were evaluated under uniaxial compression loading conducted at 37 °C in culture media with an integrated camera. Reinforced constructs showed more than a 35-fold-increase of the compressive Young's modulus. However, the compressive Young's moduli were highly strain-rate dependent. The fibre reinforcement has a particular impact on the Poisson's ratio of the composite constructs, decreasing from values of approximately 0.4 to 0.01. The high interfacial surface area between the fibre structure and the hydrogel matrix is believed to be one of the main factors responsible for the significant increase in the mechanical properties of the constructs. In summary, we have found that reinforcement of hydrogels with defined MEW fibre architectures achieves an outstanding increase in the mechanical properties at high strain rates.