Young Southeast Asian Leaders Initiative Act or the YSEALI Act This bill provides statutory authority for the Department of State's Young Southeast Asian Leaders Initiative. The initiative shall include an academic fellows program and a professional fellows program to bring eligible students and professionals to the United States for building practical expertise, leadership skills, and professional networks. The fellows programs shall be open to qualified individuals who are citizens and residents of a member country of the Association of Southeast Asian Nations or a country that the State Department determines to be appropriate for the programs. The State Department shall oversee all U.S.-based activities carried out under the initiative.