Neither company specified the cost of the deal but it was believed to total about $1.03 billion, Haaretz reported.
Google said the Waze development team would remain in Israel "for now," the report said.
"We're excited about the prospect of enhancing Google Maps with some of the traffic update features provided by Waze and enhancing Waze with Google's search capabilities," a statement from Google said.
Prime Minister Binyamin Netanyahu telephoned Noam Bardin, the chief executive officer of Waze, and told him, "You put Israeli technology on the global map. ... I am waiting for your next start-up, you have done exceptional work," Channel 2 reported.
Google said the company was buying Waze to help "outsmart traffic."
About 47.5 million drivers have joined Waze since its inception in 2008. The application relies on information from its users to produce its maps.
The "fast-growing community of traffic-obsessed drivers is working together to find the best routes from home to work, every day," Google said.
Bardin said on his blog the deal won't change the company
"We will maintain our community, brand, service and organization -- the community hierarchy, responsibilities and processes will remain the same."
Waze computes driving routes in real-time traffic conditions, alerting drivers to traffic accidents, road hazards, even the presence of police, developers say.