The deal centers on a set of rules, called net neutrality, that determines how Internet traffic moves over land lines and to wireless devices involving payment by Internet companies seeking a faster traffic.
Verizon will not block or slow Internet traffic over land lines but could do so to wireless devices, one source said.
The agreement comes among a series of closed-door meetings at the Federal Communications Commission involving the two companies, AT&T Inc and other Internet companies to set rules for the industry.
One source said Verizon and Google were still trying to determine when to formally announce the deal, and how to involve U.S. Representative Rick Boucher who has acted as a mediator to the talks.
Verizon and Google have worked closely in the wireless device area. Verizon Wireless, a venture between Verizon Communications and Vodafone Group Plc, depends heavily on phones based on Google's Android software for growth.
We've been working with Google for 10 months to reach an agreement on broadband policy, Verizon spokesman David Fish said.
A Google spokeswoman could not be reached for comment.
At the FCC phone, cable and Internet companies have been meeting with senior officials in an effort to reach a consensus on how Internet access should be regulated.
The FCC voted in June to collect public comments on whether the agency should reclassify broadband regulation under existing phone rules -- typically considered a stricter regulatory regime.
The FCC vote came after a U.S. appeals court ruled that the agency lacked authority to stop cable television company Comcast Corp from blocking bandwidth-hogging applications.
The public interest group Free Press and others criticized the agreement.
A deal with Verizon cements its market power, and could make it more difficult for new app developers and software entrepreneurs to reach consumers, Free Press President Josh Silver said.
AT&T said it is not a party to the deal between Google and Verizon.
We remain committed to trying to reach a consensus on this issue through the FCC process, said Jim Cicconi, AT&T's senior executive vice president legislative affairs.
(Reporting by John Poirier; Editing by Leslie Gevirtz)