We demonstrate here that 1D magnetoelectric core-shell nano-architectures can be rationally designed by a two-step procedure using the template-assisted liquid phase deposition (LPD) method. Highly crystalline BaTiO 3 nanotubes with an average diameter of 20 nm and controllable wall thickness were synthesized by immersing alumina templates into a treatment solution containing the perovskite precursors at temperatures as low as 40 o C. By a similar procedure the resulting ferroelectric nanotubes immobilized within the channels of the anodic aluminum oxide (AAO) membranes have been subsequently filled with a spinel ferrite phase, with the chemical composition Zn 1.5 Fe 1.5 O 4 yielding spinel-perovskite 1D core-shell magnetoelectric architectures. The resulting core-shell tubular nanocomposites have been synthesized and characterized structurally, morphologically and compositionally and their ferroelectric, magnetic and magnetoelectric properties have been investigated both qualitatively and quantitatively. A change from a superparamagnetic to a ferrimagnetic behavior was observed in the pristine spinel ferrite nanotubes when they have been incorporated into the spinel-perovskite core-shell nanocomposites, which clearly indicates the existence of a magnetoelectric coupling between the two ferroic phases. Moreover, the measured magnetoelectric coupling coefficient was α=1.08 V/cm•Oe, value which is superior to the values reported for similar thin film and tubular spinel ferrite magnetoelectric nanocomposites, thereby making indicating a strong strain-mediated coupling between the ferroelectric and magnetostrictive phase in the 1D core-shell nanocomposites and making these materials suitable for implementation into various functional devices.