In a statement issued by the White House, the Bidens said Champ "passed away peacefully at home" at the age of 13.
"He was our constant, cherished companion during the last 13 years and was adored by the entire Biden family," they said.
"Even as Champ's strength waned in his last months, when we came into a room, he would immediately pull himself up, his tail always wagging, and nuzzle us for an ear scratch or a belly rub. Wherever we were, he wanted to be, and everything was instantly better when he was next to us."
Champ, they said, had been the family's staunch companion during their "most joyful moments" and "most grief-stricken days."
"We love our sweet, good boy and will miss him always," the President and first lady concluded.
Champ and the Bidens' other German shepherd, Major, returned to the White House in late March after Major received some training in response to a biting incident.
Michael LaRosa, Jill Biden's press secretary, said Major was trained after he snapped at someone in the White House earlier that month.
After the incident, Joe Biden called Major "a sweet dog. Eighty-five percent of the people there love him. He just -- all he does is lick them and wag his tail."
But just days later, Major was once again the dog house after another biting incident.