Waze, an Israeli mobile satellite navigation application, is seen on a smartphone in this photo illustration taken in Tel Aviv May 9, 2013. (Nir Elias/REUTERS)

Israelis have a reputation as some of the most aggressive drivers in the world. The tanned guy with the shaved head and wraparound sunglasses leaning on his horn, three inches from your bumper? He’s in a hurry.

But even the most competitive lane-changers in Israel have fallen in love with a homegrown satellite navigation system for their smartphones, called Waze, that is helping them cope with traffic jams, speed traps, road hazards — and maybe one another.

Waze describes itself as “the world’s fastest-growing ­community-based traffic and navigation app.” It has been downloaded by 49 million people.

After weeks of rumors, Google announced Tuesday that it was acquiring Waze. Industry watchers say the price topped $1 billion, but neither party would talk numbers. An Israeli business news Web site, the Marker, reported a possible hitch: European regulators may seek guarantees that user information held by Waze not be accessible to the U.S. National Security Agency.

The voice navigation system was invented by a frustrated Israeli commuter and software designer named Ehud Shabtai, who, according to the company Web site, needed help following directions. With two partners, Shabtai founded the start-up in 2008; two years later, the Waze app was widely available for download.

Unlike traditional GPS devices, Waze is driven by “crowd-sourcing,” which creates a kind of network effect. Each phone is tracked as it travels, and the information feeds into Waze servers that analyze speed, flow and routes in real time. Or as Waze puts it: “Outsmarting traffic. Together.”

Many Israeli drivers have traditionally not been too keen on the togetherness thing. But Waze may be steering them in another direction.

“One of the features is that you can see and talk to other Wazers. There is a certain camaraderie,” said Issamar Ginzberg, a business consultant and rabbi. “It’s very interactive.”

The guidance system is popular in the United States, but here in Israel, Waze has become a kind of obsession. According to a company representative, about 90 percent of all Israeli drivers have downloaded the app. More than 1.7 million Wazers were out on Israel’s roads last month. This is a country with only 2.5 million vehicles.

“You use Waze, okay? It’s free. It’s Israeli. No problem,” said Yossi Laor, who sells electronics in West Jerusalem, adding helpfully: “Everything else is garbage.”

He had fancy GPS units for sale in his shop but essentially said: Why bother?

Newcomers to Israel are advised by friends — and complete strangers — to immediately download the app. “Waze it” has replaced “Google it” as a shorthand for getting driving instructions.

“I was used to the old Israeli method of pulling over, talking to three different people and getting three different sets of directions,” said Jay Ruderman, a former Bostonian who is now a resident of the southern Israeli town of Rehovot. “I will never go back to the old method.”

The more Wazers on the road, the better and more accurate the navigation and real-time information about traffic conditions. Waze takes this information and offers alternative routes.

The algorithms are sophisticated enough that Waze knows when cars are stopped at traffic lights versus stuck in traffic. The software speaks dozens of languages and does several accents, including an Elvis impersonation.

Wazeniks may also share real-time information to help other drivers on the road, allowing them to touch their screens when they see accidents, police or hazards. The company awards status for miles driven using the app — from “Waze Baby” to “Waze Royalty.” The app speaks both Hebrew and Arabic, and Arab Israelis use it. It also works in the West Bank — but coverage in the Palestinian territory feels spotty and less detailed, users say.

The U.S. State Department, in its travel advisory about Israel, warns that “aggressive driving is commonplace, and many drivers fail to maintain safe following distances or signal before changing lanes or making turns.” Highway safety experts here say that a hands-free sat-nav system such as Waze might help Israelis drive better.

Sure, on the downside, they might focus on the dash-mounted phone inside their car and ignore the road. But there are upsides, too.

“An Israeli guy is always searching for the fastest way, but with Waze, you’re not as aggressive. Waze tells you there’s a traffic jam? Okay, you can relax. You’re going to be 30 minutes late, like everybody else, and there’s nothing you can do about it. It’s not your fault,” said Yaakov Sheinin, director of the National Road Safety Authority and an economics professor at Tel Aviv University, who is also a Wazenik.

Sheinin speculated that Waze has contributed in some way to the dramatic improvement in road safety in Israel. Eight years ago, Israel was ranked No. 22 in fatalities for billion kilometers driven. Last year, it had reduced road deaths enough to be considered the 10th safest in the industrial world.

The gizmo might calm drivers down and make the road warrior less “me versus you,” Sheinin said.

“It’s full-on social networking on the road,” said Tal Samuel-Azran, a lecturer at the Sammy Ofer School of Communications at the Herzliya Interdisciplinary Center, joking that he has heard of users employing the app to meet members of the opposite sex in traffic — by revealing their avatars to other commuters.

Part of the attraction for Israelis, Samuel-Azran said, is that apart from being free, it’s perfect for those me-first drivers who always have to get to their destination first.

“Using Waze gives you a competitive advantage,” he said.

Booth reported from Jerusalem.