Medicare Negotiation and Competitive Licensing Act of 2019 This bill requires the Centers for Medicare & Medicaid Services (CMS) to negotiate with pharmaceutical companies regarding prices for drugs covered under the Medicare prescription drug benefit. (Current law prohibits the CMS from doing so.) The CMS must take certain factors into account during negotiations, including the clinical- and cost-effectiveness of the drug, the financial burden on patients, and unmet patient needs. If the CMS is unable to negotiate the price of a drug, such drug is subject to competitive licensing in order to further its sale under Medicare, notwithstanding existing government-granted exclusivities. Additionally, for one year after a drug is provided under a competitive license, such drug is also subject to specified price limitations; if the drug is not offered at such prices, the drug is subject to additional licensing that furthers its sale under any federal program (e.g., Medicaid).