Sunshine in Litigation Act of 1999 - Amends the Federal judicial code to require a court to enter an order (under rule 26(c) of the Federal Rules of Civil Procedure) restricting the disclosure of information obtained through discovery, approving a settlement agreement that would restrict the disclosure of such information, or restricting access to court records in a civil case only after making particularized findings of fact that: (1) such order would not restrict the disclosure of information which is relevant to the protection of public health or safety; or (2) the public interest in disclosure of potential health or safety hazards is clearly outweighed by a specific and substantial interest in maintaining the confidentiality of the information or records in question and the requested protective order is no broader than necessary to protect the privacy interest asserted.

Provides that: (1) no such order (other than an order approving a settlement agreement) shall continue in effect after the entry of final judgment unless at or after such entry the court makes a separate particularized finding of fact that such requirements have been met; (2) the party who is the proponent for entry of the order shall have the burden of proof; (3) no Federal court may approve or enforce any provision of an agreement between or among parties to a civil action, or approve or enforce an order subject to this Act, that prohibits or otherwise restricts a party from disclosing any information relevant to such civil action to any Federal or State agency with authority to enforce laws regulating an activity related to such information; and (4) any such information disclosed to a Federal or State agency shall be confidential to the extent provided by law.