Antibody-dependent cell-mediated cytotoxicity, a key effector function for the clinical efficacy of monoclonal antibodies, is mediated primarily through a set of closely related Fcγ receptors with both activating and inhibitory activities. By using computational design algorithms and high-throughput screening, we have engineered a series of Fc variants with optimized Fcγ receptor affinity and specificity. The designed variants display >2 orders of magnitude enhancement of in vitro effector function, enable efficacy against cells expressing low levels of target antigen, and result in increased cytotoxicity in an in vivo preclinical model. Our engineered Fc regions offer a means for improving the next generation of therapeutic antibodies and have the potential to broaden the diversity of antigens that can be targeted for antibody-based tumor therapy.