Allied Nations Travel Modernization Act of 2019 This bill allows a country to qualify for the Visa Waiver Program by having a low rate of visa overstays by its nationals and making certain commitments to defense spending as part of the North Atlantic Treaty Organization (NATO). A country may qualify or maintain qualification for the Visa Waiver Program if (1) the nationals of that country did not overstay their U.S. nonimmigrant visas at a rate higher than 2% during the last two fiscal years, (2) the country is a signatory to the Wales Summit Declaration and has committed for the last two fiscal years sufficient resources to meet its obligations under the declaration, and (3) the Department of State has not in the last fiscal year issued any travel advisory to that country other than exercise normal precautions . The Wales Summit Declaration is a NATO document in which signatories agree to certain commitments, including certain minimum levels on annual defense spending.