Accelerated Drug Approval for Prescription Therapies Act or the ADAPT Act This bill authorizes the Food and Drug Administration (FDA) to create an expedited drug approval process specifically for drugs that are currently approved for sale in certain countries (i.e., a European Economic Area member country, Australia, Canada, Israel, Japan, New Zealand, South Africa, or Switzerland) and meet certain criteria. Such criteria shall include establishing that (1) the drug is safe and effective, (2) all relevant U.S. patents or legal exclusivities have expired, and (3) the United States has a public health or unmet medical need for the drug. The FDA must process and review an application under this bill within 180 days of submission.