The news of their relationship, which was first reported by Vanity Fair earlier Thursday, drew denials from both.
"Right now I am focused on raising my daughter and I am not dating anyone," Earhardt, a Fox & Friends co-host, said through a network spokesperson. "As anyone at Fox News will tell you, Sean is a wonderful person and whomever he chooses to date will be extremely fortunate."
In his own statement through a spokesperson, Hannity said: “I do not discuss my personal life in public.”
But the source familiar with the situation says the two have "been seeing each other very secretively for years."
"He's very private, because he's very famous and he's very controversial," the source says, "but it's been an open secret that they have been seeing each other."
Earhardt has been recording at Hannity's home studio on Long Island, New York, and is renting a home nearby.
"They're together all the time, but in private. ... for years," the source says, "not just months."
Related Video: ‘Fox & Friends’ Star Announces Split From Husband
The source says Earhardt and Hannity have been seen together "acting flirty in off-hours" and "getting cozy in the back of" a New York City bar not far from the Fox News studios.
"And he's whisked her off on his chopper for a vacation many times," the source says.
According to Vanity Fair, Earhardt rode on Hannity's helicopter with him last August to the wedding of another Fox News host, Pete Hegseth.
Last week, Hannity and his ex-wife, Jill Rhodes, confirmed they had quietly divorced more than a year ago and separated years before that. They were together for more than 20 years.
In a joint statement to PEOPLE on June 3, the former couple said, "Sean and Jill are committed to working together for the best interests of their children. Amicable agreements were entered into over four years ago between Sean and Jill. They maintain a close relationship as parents to their children."
"Neither will have any further comments and ask for sake of their children that their privacy be respected," the statement concluded.
Hannity and former journalist Rhodes, 57, share two children: son Sean Patrick, 21, and daughter Merri Kelly, 18.
Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories
In an October 2019 interview with PEOPLE, she said she was grateful her divorce chapter “is closed,” and said she and Proctor are amicable and remain focused on bringing up their little girl together.
“We’re focusing on moving ahead and raising our daughter. We honestly wish each other nothing but the best, and we will remain friends for the rest of our lives because we share this precious, beautiful daughter together. She is our top priority,” Earhardt, who got pregnant with Hayden three months after suffering a miscarriage, said at the time. “She is the light of my life.”
Earhardt added that she and her ex-husband are “co-parenting and doing it beautifully. [Hayden] loves her mommy and loves her daddy, and we both adore her.”
The TV host also spoke to PEOPLE about the challenges of being a being a single mother, as well as her thoughts on marriage and more children down the road should she meet a new partner.
“I would love to find love again and I want to demonstrate a loving relationship for Hayden one day. But I’m not sure when that will be,” she said at the time. “I know that God will put the right man in my life if that’s his will, and he’ll do it in his time.”