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"It definitely posed challenges when he was coming at me so relentlessly and causing security issues in my life and the life of my family, but I did it," Kelly, 45, said today on "Good Morning America." "It was a test of me as a person and a professional."
Trump, now the president-elect, criticized Kelly after she questioned him about calling women "fat pigs" and "slobs" during the first prime-time Republican candidates' debate. He drew fire for later saying about her that there was "blood coming out of her wherever"; the next day, he said he was referring to her nose.
Kelly, the host of Fox's "The Kelly File," said that Trump can be "vindictive" and that there is "no question" he is "thin-skinned" and "can be mean-spirited."
She met with him in Trump Tower in New York City during the campaign and said that proved a turning point in their professional relationship.
"My own experience with him proves he's able to let things go if he so chooses," she said. "He came after me like a dog with a bone for nine months, but finally, when I went to see him at Trump Tower — and believe me, I was not conciliatory towards him — we got past it."
Kelly writes about Trump and her former boss Roger Ailes in hew newly released memoir, "Settle for More."
She said the meeting at Trump Tower started with a "bizarre" greeting.
"I went over there, and I walked in. He gave me a nice greeting. He hugged me," Kelly said on "GMA." "It was bizarre to be hugging this man who had tried to torment me for nine months and who had endangered my security."
"I accepted it for the gesture it was, which I think was a goodwill gesture to try to say if not 'I'm sorry,' then 'Let's move on,'" she said. "I neither apologized to him, nor did he apologize to me."
Kelly described the meeting as "very cordial" and said it worked as a "reset of sorts" for her and Trump.
She is now watching with the rest of the world as he appoints his White House aides and advisers. He has so far named Republican National Committee Chairman Reince Priebus as his chief of staff and Stephen Bannon as his senior counselor and chief West Wing strategist.
"Trump is entitled to surround himself with the people who he most trusts," said Kelly, who credited Bannon with understanding "working class Americans who have had it with Washington and the so-called establishment."
"What we're being told is Steve Bannon will really have the ear of Trump," Kelly said. "I don't know what that means for Reince Priebus."
The appointment of Bannon has drawn criticism because of his past leadership of Breitbart News. Some critics have said Trump is bringing a white supremacist into the White House with the appointment of Bannon.
I don't know that there's evidence of that," Kelly said. "What his defenders say is he's not responsible for every single headline that went up on Breitbart while he was the executive chairman and that that website is known for being provocative and so they're looking for clicks."
"Now, it definitely appeals to a segment of the so-called alt-right, which includes some white supremacists, but I don't know that you could tar the entire team with that brush or Steve Bannon with that brush," she said. "Having said that, there is no question this man is controversial."