Johnson & Johnson plans to break up into two companies, splitting off the $15-billion-a-year division that sells Band-Aid bandages, Tylenol medicines and Johnson’s Baby Powder in a shift indicating just how much healthcare has changed since the company helped pioneer the industry.

The world’s largest health-products company by sales will separate its high-margin but less predictable prescription-drug and medical-device businesses from its storied but slower-growing consumer group, creating two publicly traded companies.