In the coming days, Biden's fellow Democrats "will undertake a transparent and orderly process to move forward as a united Democratic Party with a candidate who can defeat Donald Trump in November," chairman Jaime Harrison said in a statement.
Here's a look at how replacing the 81-year-old could work.
Chaotic convention?
To designate a formal nominee, delegates chosen from all 50 states, the U.S. capital and overseas territories attend their party's summer nominating convention to officially anoint a candidate.
Biden overwhelmingly won the primary votes, and the party's roughly 3,900 delegates heading to the convention -- scheduled to begin August 19 in Chicago -- are pledged to back him.
Party leaders had previously planned to formally nominate Biden via a virtual roll call ahead of the convention, due to potential legal issues regarding Ohio.
With Biden exiting, it is unclear if or when that early meeting will occur, but naming his replacement will ultimately fall to the delegates.
"Our delegates are prepared to take seriously their responsibility in swiftly delivering a candidate to the American people," Harrison said, adding that the "process will be governed by established rules and procedures of the Party."
The last-minute change could bring U.S. politics back to the old days, when party bosses jostled to pick a nominee through deal-making in smoke-filled back rooms and endless rounds of voting.
On March 31, 1968, then-president Lyndon Johnson made the shock announcement in the middle of the Vietnam War that he would not seek reelection.
The move -- though announced far earlier in the campaign than Biden's -- turned that year's convention, also in Chicago, into a political crisis, with protesters in the streets and left-leaning delegates angry at the pro-war stance of party-picked candidate Hubert Humphrey.
Following that debacle, states more widely embraced the primary process and conventions have become well-oiled affairs whose outcomes are effectively known in advance.
Who might step in?
Immediately after Biden's disastrous performance against Trump in a June 27 debate, which supercharged the concerns over his age and ability to beat the Republican at the polls, Democrats had circled their wagons around the president -- at least when speaking on the record.
All of that dissolved as time went on, with increasingly senior party leaders publicly questioning the viability of the incumbent's candidacy.
A natural -- but not automatic -- pick to take Biden's place would be Vice President Kamala Harris, whom Biden quickly endorsed Sunday -- and who vowed to pick up the baton.
"With this selfless and patriotic act, President Biden is doing what he has done throughout his life of service: putting the American people and our country above everything else," she said in a statement.
"I am honored to have the president's endorsement and my intention is to earn and win this nomination...."I will do everything in my power to unite the Democratic Party -- and unite our nation -- to defeat Donald Trump."
Former president Bill Clinton and ex-secretary of state Hillary Clinton also threw their support behind Harris.
Sent in to put out the fire after Biden's lackluster performance at the debate, the 59-year-old conceded Biden had been "slow to start" against Trump but had "finished strong."
Otherwise, any of a number of strong Democratic politicians -- Governors Gavin Newsom of California, Gretchen Whitmer of Michigan and Josh Shapiro of Pennsylvania have been mentioned -- might be called on.
Third-party chances?
With Biden dropping out, could a strong third-party hopeful emerge? So far, no independent candidate is posing any danger to the United States' dominant two-party system.
In 1992, Texas billionaire Ross Perot, running as an independent, managed to win nearly 19 percent of the popular vote.
But in the end, because of the way the country's electoral system works, he did not receive a single one of the votes that matter most: those of the 538 members of the Electoral College that ultimately decide the winner.