The deal, which is expected to close in the second quarter, will combine Yahoo's search, email and messenger assets as well as advertising technology tools with its AOL unit.
Verizon had been trying to persuade Yahoo to amend the terms of the agreement to reflect the economic damage from two cyber attacks.
Under the amended terms, Yahoo and Verizon will split any future liabilities and costs that arise from the data breaches.
In late January, more than a month after Yahoo had disclosed its second breach, Verizon Chief Executive Lowell McAdam sat with two of his top lieutenants in the company’s Basking Ridge, N.J., offices and weighed his options, according to people familiar with the matter.
The Wall Street Journal reports McAdam still felt owning Yahoo made sense—and further delay would prevent Verizon from getting going on its ambitious plans to take on Alphabet Inc.’s Google and Facebook Inc. in digital advertising. Verizon is looking for sources of growth as its core cellphone business matures and faces tough competition from rivals.
Mr. McAdam decided to proceed with the deal—but Verizon would need a discount because of the uncertainty, the people said.