He says it's "in the best interest of my party and the country" – but will stay on for the final six months of his term. Biden endorses Kamala Harris, his vice-president, to be the new Democratic nominee.
Harris says she intends to "earn and win" the nomination and do "everything in my power to... unite our nation to defeat Donald Trump".
Former President Bill Clinton and Hilary Clinton, who ran against Trump in 2016, also endorse Harris - saying Democrats must "fight with everything we've got to elect her".
Former President Barack Obama says Democrats will name an "outstanding nominee", but does not endorse Harris or any candidate.
First Lady Jill Biden has been supportive of her husband "whatever road he chose", her spokeswoman tells the BBC.
Biden, 81, faced increasing calls to step aside since a faltering debate performance against Trump last month. (BBC)
