Wireless phone companies and equipment manufacturers totally underestimated the potential of their own industry, says Ericsson (ERIC) CEO Hans Vestberg. Now he and his company are preparing for a totally interconnected world in which billions of consumers — and machines — talk non-stop to one another via wireless networks.

“What I’ve learned in this industry, and I’ve spent 18 years in it, is that we overestimate what happens in the next two to three years but underestimate what’s going to happen in 10 years,” says Vestberg, who became president and CEO of the Stockholm-based telecommunications equipment company on Jan. 1. He previously served as chief financial officer of the company, which last year posted about $28 billion in sales.

Vestberg says many industry executives and analysts believed wireless penetration would max out at 1 billion subscribers worldwide. At the end of 2009 there were more than 4.6 billion wireless subscriptions (some people have more than one mobile service) and Ericsson forecasts that number to grow to more than 6 billion in 2015. “That’s just enormous,” Vestberg tells Fortune. “It is beyond where we thought this industry could go.”

Still, Vestberg is cautious about the industry’s short-term prospects. Ericsson, which operates in 175 countries, was hit hard by the global economic meltdown. (Last year profits fell some 65% on flat sales.) Vestberg noted that the mood seems brighter at recent industry trade shows, including the CTIA show held in Las Vegas this month, but he declined to comment on trends in Ericsson’s portfolio. ” We are not stating anything,” he says. “We are waiting for the quarter’s results to come out.”

He does, however, offer an unabashedly upbeat view of the long-term future  In addition to the continued growth of mobile subscriptions, he enthused about a growth in mobile usage, driven by wireless broadband networks and services. Indeed, Ericsson this week released data showing that in December 2009 mobile data traffic — Internet, video and other high-throughput services — surpassed voice traffic for the first time. Non-phone consumer gadgets such as Amazon’s (AMZN) Kindle, and a new generation of devices, including the forthcoming Apple (AAPL) iPad, will add to the volume of data traversing wireless systems.

But consumers are just part of the growth trajectory for wireless data, according to Vestberg. “Our vision is that by 2020 we will have 50 billion connected devices,” he declares. He envisions a world in which billions of machines — from pacemakers to cash registers to electricity meters — are outfitted with radios that allow the gadgets to send a steady stream of information to computers. Computing giants such as IBM (IBM), Hewlett Packard (HPQ), and Cisco (CSCO) already all promote such “connected planet” strategies, offering the computers, software, and even the sensors clients would need to hook up machines and interpret the data those devices transmit.

For Ericsson, a big opportunity lies not only in selling wireless gear to increase the capacity of wireless networks but in managing and optimizing the wireless links between machines and the transmission over wireless networks to big computing centers that will crunch all that data. It is a specialty that the main purveyors of computing services lack, and a growing area for Ericsson, which actually got its start as a repair shop for telegraph equipment. In the fourth quarter, managed services accounted for nearly 30% of the company’s sales.

“For the last 10 years in the industry has been installing all this equipment around this world,” Vestberg says. “The next phase is going to be a deployment phase using all these technologies.” If Vestberg has his way, Ericsson will play as important a role in connecting machines to one another as it did in helping consumers talk to one another.

[cnnmoney-video vid=/video/technology/2010/03/29/f_tt_ericsson_vestberg_mobile.fortune]