“Winning over Senator Sanders is one thing, but Joe Biden shouldn’t think that the work is over,’’ said Evan Weber, political director for the Sunrise Movement, an organization of young climate activists that had endorsed Mr. Sanders. He added, “There is still work to do to win over progressive leaders and young people.”

In moving so quickly to embrace more of the policy ideas and political language of Mr. Sanders and the left, Mr. Biden is providing the clearest sign yet that the virus has changed the political equation and the rhythms of the election season. He also has indicated an intention to expand beyond his primary campaign message of restoring the nation and Washington to a pre-Trump era.

Progressives have been scathingly critical of that argument, saying that it neglects the many inequities in the economic, health care and immigration systems and in other areas where lower-income people struggled in the Obama era and under past presidents.

But at a moment of a presidential campaign when candidates often move to the center, this expanded message could prove perilous if progressives push Mr. Biden to make policy concessions and changes that start to concern more moderate Democrats and independent voters who do not support some planks of a far-reaching liberal agenda.

The alliance announced Monday was a sharp departure from the drawn-out, often-acrimonious process of reconciliation between Mr. Sanders and Hillary Clinton in the 2016 presidential race. And it makes good on the promise Mr. Sanders has been making for months: That he would support the eventual Democratic nominee and do everything he could to defeat Mr. Trump, whom he has called “the most dangerous president” in modern times.

Former Senator Christopher J. Dodd, Democrat of Connecticut and a Biden supporter, said the quick cooperation was a reflection of the friendly personal relationship the two men enjoyed. Mr. Sanders was said to be greatly appreciative that Mr. Biden did not try to rush him out of the race.

“A lot of people think it’s old-fashioned, being polite to people, listening to people, paying attention to them,” he said. “It’s still important to people. Personal relationships mean a lot.”