By Agence France-Presse
Daniels, whose real name is Stephanie Clifford, claims she had an affair with Trump in 2006 and was paid the sum as part of a "hush agreement."
"They funneled it through a law firm and the president repaid it," Giuliani, who recently joined Trump's legal team, told Fox News host Sean Hannity.
"That was money that was paid by his lawyer, the way I would do, out of his law firm funds or whatever funds, it doesn't matter. The president reimbursed that over a period of several months," Giuliani said.
He added that the payment did not represent a campaign financing violation because it was "not campaign money."
Trump had previously denied all knowledge of the payment to Daniels, before admitting last week that Cohen struck a "deal" with the porn star on his behalf.
Her lawyer Michael Avenatti reacted swiftly to the revelation, calling out the US president over his "lies."
"We predicted months ago that it would be proven that the American people had been lied to as to the $130k payment and what Mr. Trump knew, when he knew it and what he did in connection with it," he wrote.
"Every American, regardless of their politics, should be outraged by what we have now learned."
Daniels filed a lawsuit against the president on Monday for defamation after he trashed her claim that she had been threatened by a man representing Trump in 2011.
Cohen, meanwhile, has legal troubles of his own.
The FBI raided his home and office in early April and seized documents and other material in connection with a criminal investigation.
The nature of the alleged criminal wrongdoing by Trump's personal attorney has not been revealed.