Romney, 63, described her "darkest hour" to Roberts, telling her she had "ripped up all the pictures" taken of her around the time she was diagnosed.
"Now I can relate to someone who's going through a really hard time," she said. "I can say I know how you feel like. I know how hard it is."
"It humbled me," she said of the illness, now in remission, adding that her husband would not have sought the nomination if she remained ill.
She also used the interview to take shots at President Obama, whose campaign recently accused her husband of a possible felony for allegedly lying about his resignation from the post of CEO of Bain Capital.
"I believe it was beneath the dignity of the office of the president to do something as egregious as that," she said. "To attack someone on that level is, I believe, beneath his dignity."
Romney has often been called her husband's "secret weapon," after speaking publicly about overcoming breast cancer, depression and multiple sclerosis.