Early Pell Promise Act This bill amends title IV (Student Assistance) of the Higher Education Act of 1965 to authorize the Department of Education to carry out a program of grants to state educational agencies under which a student who is in eighth grade and is eligible for a free or reduced price lunch under the Richard B. Russell National School Lunch Act may be provided a commitment to receive a Federal Pell Grant early in the student's academic career. Pursuant to such a commitment, the student shall receive a Pell Grant during the first two years of attendance at an institution of higher education (IHE) as an undergraduate if the student: files the FAFSA form during the senior year of secondary school and the succeeding year, and enrolls at the IHE not later than three years after receiving a secondary school diploma or after release from the Armed Forces. A student may not receive the early Pell Grant for a succeeding year if the expected family contribution for either year is more than twice the threshold amount for Pell Grant eligibility for that year.