A novel reactive flame-retardant (FR), phosphorus-modified tetraethylenepentamine (TEPA-m-MVP), was prepared via aza-Michael addition process, using dimethyl vinylphosphonate (MVP). TEPA-m-MVP was successfully covalently introduced into the structure of the epoxy system, into the epoxy resin matrix synthesised from tetraethylenepentamine (TEPA) and diglycidyl ether bisphenol A (DGEBA) reaction, leading to the development of a flame-retardant epoxy resin (FR-EP). The curing behaviour, mechanical properties, thermal stability and flame-retardant behaviour of FR-EP samples were investigated and compared to the behaviour of the neat epoxy resin (EP). FR-EPs showed an increase in glass transition temperature (Tg), from 120 to 147 °C upon integrating TEPA-m-MVP into the epoxy resin structure, while the value of the E modulus remained unaffected. Furthermore, FR-EP-2%P sample with the optimal P content, approximately 2 wt%, displayed excellent flame-retardant properties. In comparison to EP, total heat release (THR) and peak heat release rate (pHRR) for FR-EP-2%P decreased from 22.6 to 15.3 kJ.g−1 and from 1557 to 572 kW.m−2, respectively. In addition, an interesting impact of the crosslinking density of FR-EP samples on the fire behaviour was observed. This work presents a new strategy for the simultaneous modification of the flame retardancy and mechanical properties of epoxy systems.