In one aspect, a bearing assembly for supporting a rotor shaft relative to a support structure of a gas turbine engine may generally include a bearing including an outer race and an inner race, an outer bearing housing configured to extend radially between the outer race of the bearing and the support structure of the gas turbine engine and an inner bearing support configured to extend radially between the inner race of the bearing and the rotor shaft. In addition, the outer bearing housing and the inner bearing support each include at least one radially extending spring arm such that the outer bearing housing and the inner bearing support collectively form two springs coupled in series between the support structure and the rotor shaft.