The NSA's main tool to exploit such data links is a project called MUSCULAR and operated jointly with the agency's British counterpart, GCHQ.
The two agencies "are copying entire data flows across fiber-optic cables that carry information between the data centers of the Silicon Valley giants," the newspaper reported.
In a statement provided to the newspaper, Google said it is "troubled by allegations of the government intercepting traffic between our data centres," and not aware of the activity.
A Yahoo spokeswoman told the daily that the company has not given access to its data centers to the NSA or to any other government agency.
Under another disclosed programme coded "PRISM," the NSA has already gathered huge volumes of online communications records by legally compelling US technology companies, including Yahoo and Google. The program is authorized under the Foreign Intelligence Surveillance Act and overseen by the Foreign Intelligence Surveillance Court.