The U.S. Food and Drug Administration has no regulatory authority over cosmetics across consumer markets. Certain ingredients are prohibited regardless of product type, but there is no FDA pre-market approval required to sell cosmetics to consumers.
As stated on the FDA.gov website:
Cosmetic firms and manufactures are not required to have any sort of FDA license to operate; however, the FDA does encourage all companies to participate in the Voluntary Cosmetic Registration Program (VCRP). This program alerts the FDA to any new products released and provides information such as products ingredient lists as well as distributor and manufacturer information. This voluntary program in conjunction with independent panels such as the Cosmetic Ingredient Review (CIR) assists in the monitoring of cosmetics currently on the market. In addition to reviewing recorded information the FDA can inspect cosmetic manufactures per the FD&C Act to ensure compliance with the law.