Billionaire investor Peter Thiel is relocating his home and personal investment firms to Los Angeles from San Francisco and scaling back his involvement in the tech industry, people familiar with his thinking said, marking a rupture between Silicon Valley and its most prominent conservative.

Mr. Thiel has also discussed with people close to him the possibility of resigning from the board of Facebook Inc., the people familiar with his thinking said. His relationship with the social-networking company—where he has been a director...