An emotional Joe Biden won a huge ovation as he gave a farewell speech at the Democratic National Convention in Chicago on Monday, after Kamala Harris made a surprise appearance to thank him for being an "incredible" US president.

"I love you," the tearful 81-year-old told the crowd to deafening cheers, less than a month after dropping out of the White House race against Donald Trump and passing the torch to his vice president.

Biden took to the stage to chants of "We love you Joe" from the same party which had pushed him out over concerns about his age, in one of the biggest political shocks in US political history.

"We both know we have more to do, but we're moving in the right direction," he said, referring to himself and the 59-year-old Harris, who, in the space of a few breathtaking weeks, has turned the presidential race upside down.

America's first female, Black and South Asian vice president has injected new life into the Democratic Party and wiped out Republican rival Donald Trump's lead in the polls.

She heaped lavish tribute on Biden, even breaking with tradition to speak on the first night of the convention in praise of her boss.

"I want to kick us off by celebrating our incredible president Joe Biden," said Harris.

"We are forever grateful to you."

As he has been so often in his five-decade-long political journey, Biden was surrounded by family, with wife Jill Biden and their daughter Ashley introducing him.

"Joe and I have been together for almost 50 years. And still, there are moments when I fall in love with him all over again," the first lady said.

The Democrats are in an exuberant mood in Chicago, daring to hope for victory in November that seemed inconceivable just weeks ago after Biden's disastrous debate against Trump.

But Monday's first night of the convention was an emotional one on many levels, and for many of the key players.

Hillary Clinton, who lost against Trump in 2016 in her own bid to become America's first woman president, backed Harris to finally break the glass ceiling.

"Something is happening in America, you can feel it -- something we've worked for and dreamed of for a long time," the former secretary of state and first lady said.

Harris will formally accept the party's nomination on the final day Thursday, in her biggest chance yet to define her candidacy in front of a huge audience of tens of millions of American voters.

Her star turn will cap a week where the biggest names from the party's past will endorse her as its future, with former president Barack Obama speaking on Tuesday, and ex-president Bill Clinton introducing Harris's running mate Tim Walz on Wednesday. (Agencies)