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4 year oldAccelerating his momentum in the race, the former US vice-president beat Mr Sanders in both states by wide margins.
Arizona was also voting on Tuesday, though its polls have not yet closed.
Mr Biden is the favourite to become the Democratic candidate who will face President Donald Trump in November.
Will Joe Biden's record come back to haunt him?
With most Florida precincts reporting, Mr Biden led Mr Sanders by more than 61% to about 23%, according to the Associated Press news agency.
In Illinois, with over a third of Illinois precincts reporting, Mr Biden led Mr Sanders by more than 58% to around 37%.
Florida was the biggest prize of the night, awarding 219 of the 1,991 delegates needed to secure the Democratic presidential nomination.
Mr Trump won the traditional battleground state by 1.2 percentage points in the 2016 presidential election.
The former US vice-president is hoping to build an unassailable lead in the race for the Democratic leadership after scoring victories in 16 of the last 21 state contests.
His victory last month in South Carolina - his first ever primary win in three campaigns for president - revived his faltering campaign.
According to opinion polling, most Florida voters said electability was a priority for them.
About three in four said Mr Biden would have a better chance of beating Mr Trump, a Republican. Just one in five said the same of Mr Sanders.
Older voters were more likely to say they supported Mr Biden.
Nearly half of Florida's voters said Mr Sanders' stances were too liberal.
Speaking from his home in Wilmington, Delaware, to comply with US anti-coronavirus advice against gatherings, Mr Biden said: "Our campaign has had a very good night."
But he focused largely on the outbreak sweeping the US, striking a unifying tone as he said: "The coronavirus doesn't care if you're a Democrat or a Republican... we're all in this together."
Mr Sanders hosted an online address from Washington DC, but he did not refer to the primaries, nor did he drop any hints about the future of his campaign.
He instead talked about the coronavirus crisis, outlining proposals to address the pandemic, which he said would cost some $2tn.
One of his campaign officials said the candidate was not expected to speak publicly again on Tuesday night.
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