We demonstrate electrical control of ferromagnetism in field-effect transistors with a trilayer quantum well (QW) channel containing an ultrathin n-type ferromagnetic semiconductor (In,Fe)As layer. A gate voltage is applied to control the electron wavefunctions {phi}i in the QW, such that the overlap of {phi}i and the (In,Fe)As layer is modified. The Curie temperature is largely changed by 42%, whereas the change in sheet carrier concentration is 2 - 3 orders of magnitude smaller than that of previous gating experiments. This result provides a new approach for versatile, low power, and ultrafast manipulation of magnetization.