Border Law Enforcement Relief Act of 2009 - Authorizes the Attorney General to award grants on a competitive basis to eligible law enforcement agencies to assist such agencies in addressing border-related criminal activity within their jurisdictions. Defines "eligible law enforcement agency" as a tribal, state, or local law enforcement agency located or performing duties in a county that is within 100 miles of the Mexican or Canadian border or a county that has been designated by the Attorney General as a high impact area.