Student Achievement Act of 1999 - Authorizes the Secretary of Education to award grants to high-need, low-performing local educational agencies (LEAs) for remedial education programs to help kindergarten through grade 12 students, who are failing or at risk of failing, to meet State achievement standards in the core academic curriculum.

Requires applicant LEAs, as a condition of receiving such funds, to: (1) adopt a policy prohibiting the practice of social promotion; (2) adopt a policy requiring that all kindergarten through grade 12 students be subject to State achievement standards in the core academic curriculum at key transition points to be determined by the State; (3) use tests and other indicators, such as grades and teacher evaluations, to assess student performance in meeting such standards at such points; (5) provide remedial education for all students not meeting such standards; and (6) have substantial numbers of low-performing students.

Authorizes appropriations.