The increasing awareness of treatment effect heterogeneity has motivated flexible designs of confirmatory clinical trials that prospectively allow investigators to test for treatment efficacy for a subpopulation of patients in addition to the entire population. If a target subpopulation is not well characterized in the design stage, it can be developed at the end of a broad eligibility trial under an adaptive signature design. We propose new procedures for subgroup selection and treatment effect estimation (for the selected subgroup) under an adaptive signature design. We first provide a simple and general characterization of the optimal subgroup that maximizes the power for demonstrating treatment efficacy or the expected gain based on a specified utility function. This characterization motivates a procedure for subgroup selection that involves prediction modeling, augmented inverse probability weighting, and low-dimensional maximization. A cross-validation procedure can be used to remove or reduce any selection bias that may result from subgroup selection, and a bootstrap procedure can be used to make inference about the treatment effect in the selected subgroup. The proposed approach is evaluated in a simulation study and illustrated with a real example concerning human immunodeficiency virus infection. The main ideas of this work generalize easily to other designs that involve data-driven subgroup selection, including adaptive enrichment designs.