If you take a stroll around Coca-Cola headquarters in Atlanta and peek into people’s offices, you’ll notice that some of the walls are festooned with silver-embossed blue ribbons. Charles Miller, for one, has more than 20 of them, along with several other awards, all from Toastmasters International. Coke KO started an in-house Toastmasters club way back in 1972. But Miller, who is manager of financial systems and accounting, got involved just three years ago. “I thought I was a pretty good communicator when I went in,” he says. “But it turned out there was a lot to learn.”

Toastmasters isn’t new, of course—the nonprofit has been around for 91 years, and now has more than 300,000 members in 14,650 local chapters worldwide—but it’s lately been growing like crazy inside U.S. companies. About one-third of the Fortune 500, including Apple AAPL , AT&T T , Exxon Mobil XOM , Google GOOG , Microsoft MSFT , and Disney DIS , now sponsor their own clubs. Bank of America BAC has 60 of them. During the past year, according to Toastmasters, more than 790 new ones have sprung up.

The reason: Although it’s best known for its longtime mission of helping people be more proficient (and less panicky) public speakers, the organization has recently expanded its activities to include leadership training.

The Coca-Cola club, dubbed 310 North for one of the company’s original street addresses, is typical. The group meets every Thursday morning at 7:30 for an hour and half. Everyone gets a chance to give a short impromptu presentation and a brief prepared speech. Then attendees evaluate each other’s talks, including “what was effective and what could be improved,” says Miller.

Beyond that traditional agenda, however, the club has lately added conferences, workshops, and town-hall-style Q&A sessions with top company executives, all aimed at polishing up-and-comers’ people skills, including how to run productive meetings and encourage frictionless teamwork. Miller says that he’s learned from Toastmasters “how to be a better listener, and how to ‘read’ people and respond in the right way.”

It’s no coincidence that these corporate clubs are multiplying just as millennials are flooding the workplace. Often, their bosses suggest they sign up. “The Toastmasters program does not specifically tell young people about the hazards of too much reliance on texting and email,” notes Suzanne Frey, a Toastmasters manager. But, once they start going to meetings where their presentations are rated by peers and higher-ups, she adds, “they ‘get it’” and “start realizing what effective workplace communication looks like.”

Or, as Miller puts it, “A text or an email is fine for sending a few facts, but to connect and collaborate on a deeper level, in-person conversation is really irreplaceable.”