Falwell had been on indefinite paid leave since August 7, after he posted to Instagram then deleted a mildly racy photo from a yacht costume party.
She also spoke as part of a panel with her husband and Donald Trump Jr at last year's Conservative Political Action Conference, the signature annual gathering of USA conservatives.
In his statement, Falwell said he and his wife met the man she had an affair with during a vacation over eight years ago.
One 2012 text message, which Mr Granda said came from Mrs Falwell, read in part: "Right now I am just missing you like insane ..."
Granda reportedly shared a screenshot of a FaceTime call he had with the Falwells in 2019 in which "Becki was naked as the two discussed their relationship while Jerry peeked from behind a door".
In subsequent years, the sexual relationship continued, Mr Granda said.
"Whether it was immaturity, naïveté, instability or a combination thereof, it was this "mindset" that the Falwells likely detected in deciding that I was the ideal target for their sexual escapades, " he told Reuters.
A prominent supporter of US President Donald Trump, he took over at the college after the death of his father, Jerry Falwell.
Mr. Falwell said his wife had an affair with Mr. Granda, but he had not taken part and accused Mr. Granda of trying to extort them.
Mr Falwell's statement to the Washington Examiner did not mention Mr Granda's allegation of a love triangle.
But the alleged paramour, Giancarlo Granda, told Reuters a different story.
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BECKI:"He's like telling me every time he hooks up with people".
Politico reporter Maggie Severns said earlier tonight that Falwell is now saying, "I have not resigned". Now 29, he described the liaisons as frequent, quote, "multiple times a year", and said the encounters took place at hotels in Miami and NY and at the Falwells home in Virginia.
Some time later, he claimed, the man "began threatening to publicly reveal this secret relationship with Becki and to deliberately embarrass my wife, family, and Liberty University unless we agreed to pay him substantial monies".
Mr Falwell Sr founded the university in the 1970s as well as the conservative Moral Majority movement.
This remains a very big and very important story because it's not just or even mainly about Falwell but about the President of the United States and his path to power.
In June he apologised after deleting a much-criticised tweet that showed one person in black face and another in a Ku Klux Klan hood and robe.
The Christian school in Lynchburg, Virginia, will issue a statement soon, Liberty University spokesman Scott Lamb said.
In the photo, Mr Falwell is holding a cup of dark liquid and has one arm around a woman whose shorts are also unzipped. He also said he was "not involved" in his wife and Granda's affair.
Liberty University President Jerry Falwell Jr. on Monday denied he is stepping down from his position amid multiple public scandals. No official reason has yet been given for his departure.
Falwell had been on a leave of absence as leader of the Christian school.
He also shared a screenshot of a text from 2012 in which Becki Falwell allegedly told him: "Right now I am just missing you like insane". The university said a statement would be "forthcoming".