The 69-year-old first lady bonded with Clarkson, 38, during Thursday's episode of the talk show. The episode marked Biden's first solo TV interview since her husband, President Joe Biden, was inaugurated in January.
Biden was previously married to Bill Stevenson from 1970 to 1975 and married Joe Biden in 1977. Clarkson split from her husband, Brandon Blackstock, in June after nearly seven years of marriage.
On The Kelly Clarkson Show, Biden offered Clarkson advice on life and love after divorce.
"This is what I would say to you if I were your mother," she told Clarkson. "You know, my mother always said to me, 'Things are going to look better tomorrow, and if you can take one day at a time, things will get better."
Biden said her divorce ended up leading to her meeting Joe Biden and falling in love. The couple have one daughter, Ashley, 39.
"I look back on it now and I think, you know, if I hadn't gotten divorced I never would've met Joe. I wouldn't have the beautiful family I have now," Biden said. "So I really think things happen for the best.
"I think over time, you heal," she added. "You're gonna be surprised, and I can't wait until that day comes for you."
Clarkson said on her show in September that she didn't see her divorce coming. Clarkson has two children, daughter River Rose, 6, and son Remy Alexander, 4, with Blackstock, who has two other children from his previous marriage.
"What I'm dealing with is hard, because it involves more than just my heart. It involves a lot of little hearts. We have four kids," the singer said.
"And divorce is never easy. And we're both from divorced families, so we know the best thing here is to protect our children and their little hearts," she added.
On Thursday's show, Biden also shared what fun thing she's looking forward to in a post-COVID world.
"I don't know, maybe go have a martini and some french fries," she said.