Final answer:
The Occupational Safety and Health Act directs the Secretary of Labor to help federal agencies establish safety and health programs, creating OSHA to ensure safe working conditions.
Step-by-step explanation:
The legislation that directs the Secretary of Labor to coordinate and consult with all federal agencies to help them establish safety and health programs is the Occupational Safety and Health Act (OSH Act). This act was signed into law by President Richard M. Nixon on December 29, 1970. It created the Occupational Safety and Health Administration (OSHA), which is part of the United States Department of Labor. OSHA's mission is to ensure safe and healthful working conditions for working men and women by setting and enforcing standards and providing training, outreach, education, and assistance. Section 19 of the OSH Act specifically details federal agency safety programs and responsibilities, mandating coordination and consultation to establish comprehensive workplace safety and health programs.