College Completion and Success Act This bill amends the Higher Education Act of 1965 to modify the amount of federal student assistance provided to an institution of higher education (IHE) if a student withdraws from the IHE. Under current law, an IHE receives all of a student's financial assistance after the student completes 60% of the period of enrollment (e.g., semester). This bill requires a student to complete 100% of the period of enrollment before an IHE receives all of the student's financial assistance.