An elliptically shaped electromagnetic vibration energy harvester is presented for two- and one-dimensional motions with the easy tuning of the resonance frequency. The harvester consists of a free-to-move ring-shaped permanent magnet with radial magnetization, a set of cube magnets distributed elliptically in a fixed holder, and two coil windings located above and below the harvester. When the device is exposed to vibrations, the free-to-move ring magnet moves until the magnetic restoring force from the fixed cube magnets pushes it back while inducing an electromagnetic force on the fixed coils. The performance of the device is characterized using an XY-shaker, whose frequency is swept from 1 Hz to 10 Hz with motion amplitudes of 2 mm and 4 mm on both axes simultaneously. Unlike 1-D harvesters, the resulting output power shows two resonant frequencies at 4.5 Hz and 7 Hz, at which the harvester can generate around 1.5 mW. The device also displays a nonlinear hardening resonator behaviour. Finally, 1D vibration experimental results show that the output power of the prototype depends on its angular position with respect to the motion direction of the vibration source, reaching a maximum at an angular position of 45 degree.