Magic Mushrooms. LSD. Ketamine. The Drugs That Power Silicon Valley.

Elon Musk takes ketamine. Sergey Brin sometimes enjoys magic mushrooms. Executives at venture-capital firm Founders Fund, known for its investments in SpaceX and Facebook, have thrown parties that include psychedelics.

Routine drug use has moved from an after-hours activity squarely into corporate culture, leaving boards and business leaders to wrestle with their responsibilities for a workforce that frequently uses. At the vanguard are tech executives and employees who see psychedelics and similar substances, among them psilocybin, ketamine and LSD, as gateways to business breakthroughs.

“There are millions of people microdosing psychedelics right now,” said Karl Goldfield, a...