A piezoelectric energy harvester is an electromechanical device that converts ambient mechanical vibration into electric power. Most existing vibration energy harvesting devices operate effectively at a single frequency only, dictated by the design of the device. This frequency must match the frequency of the host structure vibration. However, real world structural vibrations rarely have a specific constant frequency. Therefore, piezoelectric harvesters that generate usable power across a range of exciting frequencies are required to make this technology commercially viable. Currently known harvester tuning techniques have many limitations, in particular they miss the ability to work during harvester operation and most often cannot perform a precise tuning. This paper describes the design and testing of a vibration energy harvester with tunable resonance frequency, wherein the tuning is accomplished by changing the attraction force between two permanent magnets by adjusting the distance between the magnets. This tuning technique allows the natural frequency to be manipulated before and during operation of the harvester. Furthermore the paper presents a physical description of the frequency tuning effect. The experimental results achieved with a piezoelectric bimorph fit the calculated results very well. The calculation and experimental results show that using this tuning technique the natural frequency of the harvester can be varied efficiently within a wide range: in the test setup, the natural frequency of the piezoelectric bimorph could be increased by more than 70%.