Biopolymers are good carrier materials in relation to efficient release sustainability for encapsulated drugs. In particular, electrospun polymer/composite fibre membranes can offer greater benefits owing to their competitive release features as well as large specific surface areas. In this study, multiple electrospun nanofibre membrane systems were utilised including different material systems such as poly(lactic acid) (PLA), poly(ε-caprolactone) (PCL), and PCL/magnetic nanoparticle (MP) composites loaded with tetracycline hydrochloride (TCH) as a therapeutic compound for their potential use in drug delivery applications. Such electrospun nanofibres were investigated to understand how composite constituents could tailor surface morphology for drug release control and biodegradation effect of PCL electrospun nanofibers on a long term for different drug release systems. Fibre diameter appeared to be decreased considerably with the addition of TCH drug. It was also evident that average fibre diameter was reduced when embedding MPs owing to the enhancement of solution conductivity. The encapsulation of TCH drug was found to be effective, as evidenced by Fourier transform infrared (FTIR) spectra. Thermogravimetric analysis (TGA) data revealed no significant change in the thermal stability of PCL with the inclusion of TCH and MPs. However, the use of TCH to PLA delayed the thermal degradation. Glass transition temperature (
T
g
) and melting temperature (
T
m
) of PCL were decreased with the inclusion of MPs and TCH. The degree of crystallinity (
X
c
) for PCL diminished when incorporated with MPs. Additional TCH to PLA, PCL, and PCL/MP nanocomposites resulted in a moderate decrease in
X
c
. TCH might be dispersed in an amorphous state within nanofibre membranes. Over the short-term periods, it was clearly seen that TCH release from PCL nanofibre membranes was higher as opposed to PLC/MP and PLA counterparts. On the contrary, such a drug release from PLC membranes became relatively slow owing to its high
X
c
. Further, the mass loss results were consistent with those obtained from in vitro drug release. Overall, TCH release kinetics of PCL/TCH nanofibre membranes were better estimated by Zeng model as opposed to PLA/TCH counterparts.