Accelerating his momentum in the race, the former US vice-president made a clean sweep in all three states.
Mr Biden appealed for support directly to Sanders supporters.
With his hat-trick, Mr Biden took another big stride towards becoming the Democratic candidate who will face President Donald Trump in November.
What are the results so far?
With most Florida precincts reporting, Mr Biden led Mr Sanders by nearly 62% to about 23%, according to the Associated Press news agency.
In Illinois, with most precincts reporting, Mr Biden led the Vermont senator by 59% to 36%.
According to partial results from Arizona, Mr Biden had a double-digit lead on Mr Sanders.
In that south-western state, Mr Biden led among white voters by 51% to 32%. Hispanic voters were more equally divided between Mr Biden (45%) and Mr Sanders (44%).
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 that traditional battleground state by 1.2 percentage points in the 2016 presidential election.
On the eve of Tuesday’s vote, Mr Biden was hoping to build on his victories in 16 of the last 21 state contests.
The former US vice-president’s triumph last month in South Carolina – his first ever primary win over three campaigns for president – resuscitated his faltering campaign.
What issues mattered to voters on Tuesday?
According to opinion polling, most voters said electability was a priority for them.
About three in four Florida voters 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.
How did the two candidates react?
In a webcam speech from his home in Wilmington, Delaware, to comply with US anti-coronavirus advice against public gatherings, Mr Biden appealed to Mr Sanders’ passionate supporters.
He said: “Let me say, especially to the young voters who have been inspired by Senator Sanders, I hear you, I know what’s at stake, I know what we have to do.”
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 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.