Drug Elimination and Justice Act - Amends the Elementary and Secondary Education Act of 1965 to authorize appropriations for grants for community learning centers for FY 1999 through 2004.

Authorizes appropriations for FY 2000 through 2002 to: (1) the Drug Court Program Office of the Office of Justice Programs of the Department of Justice (DOJ) to carry out a pilot program to establish a Federal drug court in each of ten cities in the United States that have increasing drug enforcement problems; and (2) DOJ for additional prosecutorial resources dedicated to drug enforcement in each of such cities.

Amends the Omnibus Crime Control and Safe Streets Act of 1968 to authorize appropriations for FY 2000 through 2004 for the "Cops on the Beat" program, half of which shall be used for cooperative partnerships between schools and State and local police departments to provide for the use of police officers in schools.

Amends the Controlled Substances Act to increase the minimum sentencing penalties for distributing, possessing with intent to distribute, or manufacturing a controlled substance within prescribed distances of a school or other specified facilities and to include public libraries among those facilities.