We discovered a ferromagnetic Au-Ga-Dy icosahedral quasicrystal (i QC), not only with high phase purity but also with tunable composition. The isothermal magnetization of the polycrystalline ferromagnetic i QC was closely investigated and the mean-field-like nature of the ferromagnetic transition is elucidated. Moreover, the maximum Weiss temperature (θ_{p}) of the i QCs was found at the electrons-per-atom (e/a) ratio of 1.70 being well consistent with those of ACs, validating tunability of the magnetic properties of i QCs on the basis of θ_{p}-e/a scheme for the first time. Thus, the present work provided direct evidence that the magnetism of the i QCs depends on the e/a ratio or the Fermi energy, paving the way for future studies on various exotic magnetic textures formed on a quasiperiodic lattice through the e/a ratio.