Americans now officially drink more bottled water than soda. It’s a shift that decades ago might have seemed unthinkable—that consumers would buy a packaged version of something they could get free from a tap. But bottled-water sales have been growing in the U.S. ever since the arrival of Perrier in the 1970s. The gains accelerated in recent years amid concerns about the health effects of sugary drinks and the safety of public-water supplies.

Bottled-water consumption in the U.S. reached 39.3 gallons per capita last year,...