Calling her a "lovely lady", Mr Biden told reporters: "99 years old - as my mother would say, God love her!"
First Lady Jill Biden added: "Who didn't love Betty White?"
Tributes also poured in from US actors who worked with White during her eight-decade film and TV career, including Deadpool star Ryan Reynolds.
"The world looks very different now," tweeted Reynolds about his co-star in the 2009 film The Proposal and the woman whom he jokingly referred to in media interviews as his "ex-girlfriend".
"She managed to grow very old and somehow, not old enough," he continued. "We'll miss you, Betty."
"I've heard Ryan can't get over his thing for me," White had deadpanned to People Magazine for its December issue, "but Robert Redford is The One."
Other US stars took to Twitter to send their condolences and praise her many comedic acting roles.
"A great loss to us all. We shall miss her dearly," tweeted Star Trek actor George Takei.
"I grew up watching and being delighted by her. She was playful and daring and smart," wrote Will & Grace actress Debra Messing, also calling White "a national treasure".
"What an exceptional life," posted talk show host Ellen DeGeneres. "I'm grateful for every second I got to spend with Betty White."
Steve Martin recalled a chance encounter when he was opening in 1974 for musician Linda Ronstadt in LA in a tweet to commemorate her 100th birthday.
He described feeling "elated" after White told him that she and her husband Allen Ludden came to see him "because we heard you were funny".
White also received praise online from actors Catherine Zeta-Jones, Viola Davis and Henry Winkler, as well as comedians Seth Meyers and Conan O'Brien.
"Rest in peace #bettywhite, our Golden Girl, our friend, and our neighbor," tweeted Walt Disney executive chairman Robert Iger.
"Your wit, your charm, your warmth and your smile will always be with us."
"When I was a kid, I watched 'Golden Girls' with my grandmother and I fell in love with Betty White," said actor Jennifer Love Hewitt, who starred in a 2011 Hallmark movie with White.
She described how she had kept in touch with her "idol" in the years since, often going out for pizza and drinks together.
"She was everything that you wanted her to be and more," said Love Hewitt in an emotional video.