The dogs' arrival marks the comeback of a long tradition of presidential families bringing their pets to live with them in the White House.
Champ has been part of the Biden family for more than 10 years, since December 2008, just weeks after Joe became Barack Obama's vice president-elect.
Shelter dog Major joined the family more recently after being adopted in November 2018, months before Biden announced his run for presidency in the 2020 election.
Major is the first shelter dog to move into the White House. The Delaware Humane Association, where he was adopted from, hosted a virtual "indoguration party" for Major.
But he's not the first rescue dog to live at the White House. Former president Lyndon B Johnson's daughter Luci adopted a rescue pup named Yuki who'd been abandoned by his owner at a Texas petrol station.
And former president Bill Clinton's family cat Socks was also a rescue pet.
Jill Biden told Fox 5 in Washington she would "love to get a cat", as she loves having animals around the house.
White House press secretary Jen Psaki said on Sunday evening she had no updates about whether the Bidens would get a cat.
"I'm also wondering about the cat, because the cat is going to dominate the internet whenever the cat is announced and wherever that cat is found," she said in a video on Sunday night answering questions on Twitter.
Until then, the Bidens' daughter Naomi's cat Winston holds the official title of First Cat, according to the White House pets' social media pages.
The long-held tradition of White House pets dates back to Thomas Jefferson, who had a mockingbird and several bear cubs during his presidency.
Over the years, presidential pets have become celebrities in their own right.