The magnetic and ferroelectric properties of the layered geometrically frustrated cluster compound FeTe2O5Br were investigated with single-crystal neutron diffraction and dielectric measurements. An incommensurate transverse amplitude modulated magnetic order with the wave vector q=(1/2,0.463,0) develops below T(N)=10.6(2) K. Simultaneously, a ferroelectric order due to exchange striction involving polarizable Te4+ lone-pair electrons develops perpendicular to q and to Fe3+ magnetic moments. The observed magnetoelectric coupling is proposed to originate from the temperature dependent phase difference between neighboring amplitude modulation waves.