Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices. Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena. In particular, achieving robust long-range magnetic order at the surface of the topological insulator at specific locations without introducing spin-scattering centres could open up new possibilities for devices. Here we use spin-polarized neutron reflectivity experiments to demonstrate topologically enhanced interface magnetism by coupling a ferromagnetic insulator (EuS) to a topological insulator (Bi2Se3) in a bilayer system. This interfacial ferromagnetism persists up to room temperature, even though the ferromagnetic insulator is known to order ferromagnetically only at low temperatures (<17 K). The magnetism induced at the interface resulting from the large spin-orbit interaction and the spin-momentum locking of the topological insulator surface greatly enhances the magnetic ordering (Curie) temperature of this bilayer system. The ferromagnetism extends ~2 nm into the Bi2Se3 from the interface. Owing to the short-range nature of the ferromagnetic exchange interaction, the time-reversal symmetry is broken only near the surface of a topological insulator, while leaving its bulk states unaffected. The topological magneto-electric response originating in such an engineered topological insulator could allow efficient manipulation of the magnetization dynamics by an electric field, providing an energy-efficient topological control mechanism for future spin-based technologies.