A new hybrid methodology that fully integrates the processing capabilities of the twin screw extrusion process (conveying solids, melting, dispersive and distributive mixing, pressurization, temperature profiling, devolatilization) with electrospinning is described. The hybrid process is especially suited to the dispersion of nanoparticles into polymeric binders and the generation of nanoparticle-incorporated fibres and nanofibres. The new technology base is demonstrated with the dispersion of β-tricalcium phosphate (β-TCP) nanoparticles into poly(ε-caprolactone) (PCL) to generate biodegradable non-woven meshes that can be targeted as scaffolds for tissue engineering applications. The new hybrid method yielded fibre diameters in the range of 200-2000 nm for both PCL and β-TCP/PCL (35% by weight) composite scaffolds. The degree of crystallinity of polycaprolactone meshes could be manipulated in the 35.1-41% range, using the voltage strength as a parameter. The electrospinning process, integrated with dispersive kneading disc elements, facilitated the decrease of the cluster sizes and allowed the continuous compounding of the nanoparticles into the biodegradable polymer prior to electrospinning. Thermogravimetric analysis (TGA) of the non-woven meshes validated the continuous incorporation of 35 ± 1.5% (by weight) β-TCP nanoparticles for a targeted concentration of 35%. Uniaxial tensile testing of the meshes with and without the nanoparticles indicated that the ultimate tensile strength at break of the meshes increased from 0.47 ± 0.04 to 0.79 ± 0.08 MPa upon the incorporation of the β-TCP nanoparticles. This demonstration study suggests that the new technology base is particularly suitable for the concomitant dispersion and electrospinning of nanoparticles in the generation of myriad types of functional nanofibres.