Broadwell was interviewed twice by the FBI, a U.S. official said.
The official said the investigation is not officially closed, but it appeared there will be no charges.
According to a congressional aide familiar with the matter, the House and Senate intelligence committees weren't informed that there was an FBI investigation into the situation until Friday.
"The committees are required to be kept informed of significant intelligence activities," the aide said Saturday. "If there was an official investigation that was looking, at least in part, at information that was compromising the CIA director, then I think there's a solid argument to say that the committee leadership should have been notified to at least some level of detail."
But former FBI assistant director Tom Fuentes told CNN on Monday that if, as the investigation progresses, the FBI is not "uncovering criminal activity" or a "breach of security" then "there really isn't a need" to notify members of Congress.
The FBI has "very strict protocols" about who should be notified in this type of investigation, Fuentes said.
House Majority Leader Eric Cantor, R-Virginia, knew in October about Petraeus' involvement in an extramarital affair, a spokesman for the congressman told CNN on Sunday.
Doug Heye said Cantor was tipped to the information by an FBI employee. The congressman had a conversation with the official, described as a whistle-blower, about the affair and national security concerns involved in the matter, he said.
Broadwell and Petraeus first met in 2006 at Harvard University's Kennedy School of Government, where she was a student, Broadwell wrote in the preface of the biography she co-authored on Petraeus.
She told him about her interest in studying military leadership, and he offered his help.
"I later discovered that he was famous for this type of mentoring and networking, especially with aspiring soldier-scholars," Broadwell wrote.
She traveled to Afghanistan, where she interviewed Petraeus repeatedly, sometimes on long runs that likely increased the general's respect for her.
"She probably kicked his butt," Marks said. "And it was probably the first time that had ever happened to him, so he let his guard down. He brought her in."
Such runs were a common way for Petraeus to conduct business, an adviser who worked on and off in Afghanistan with Petraeus and Broadwell told CNN. Still, some staffers were jealous of the access she had to him and the lengthy interactions they had, the adviser said.
Out of those conversations and months of other research came the best-selling book "All In: The Education of General David Petraeus."
In promoting the book, and defending it against critics who said it was too sympathetic, she frequently spoke of her unprecedented access to the general and glowingly of his character.
"I'm not a spokesperson for him, and if showing a role model to other people in the world or other readers is a repugnant thing, then I'm sorry, but I think the values that he upholds and tries to instill in his organizations are valuable and worth pointing out," she told CNN in February.
The actual affair began about two months after Petraeus took over at the CIA in September 2011, according to one Petraeus friend.
It ended about four months ago, and the two last talked about a month ago, the friend said.
The decision to end the relationship was mutual, the friend said.
Another of the former general's friends said Petraeus felt isolated after leaving the camaraderie of the military, and it made him more vulnerable.
"I think leaving the Army, the emotions, and the psychological effect impacted on him more than he thought it would," the friend said.
Broadwell, with her background in military and intelligence issues, was someone he could talk to, the friend said.
"He enjoyed her company," the friend said. "She was an attractive gal and they had things in common."