Media play is not supported on your device  Caption Bloomberg to BBC 2018: "I would like to make a difference"
His comments came after months of debate about wealth inequality in the United States, with Mr Sanders and wife Warren announced plans for steep tax increases for billionaires. Disclosure of his tax proposals in September
Mr Sanders said: "Billionaires should not exist."
Bloomberg is estimated to be worth $ 52 billion.
On Friday, President Trump hoisted Bloomberg by saying there was "no one I'd rather run against than little Michael".
Mr. Bloomberg filed his papers in Alabama later that day.
Better late than never?
Mr. Bloomberg is said to be fully aware of such delayed entry into the race posing challenges in states such as Iowa and New Hampshire, where other Democratic challengers have struggled for months.
The Bloomberg team reportedly sees a possible path through the so-called Super Tuesday contests in March, when 14 states – including California, Alabama and Colorado – will vote on a single day for their preferred White House nominees.
Mr. Bloomberg considered running for the White House as an independent candidate in both 2008 and 2016.
In March of this year, he had said he would not join race 2020.
Mr. Bloomberg and Trump, picture here playing golf in 2007, were once friendly
What happens after Alabama?
Bloomberg's advisers are reportedly preparing the paperwork for other states with the closest deadlines. Both Arkansas and New Hampshire require candidates to apply next week.
Votes between the state, known as primary and caucus, will be held from February next year to select a nominated Democratic White House.
The final winner will be crowned at the Wisconsin Conference in July. He or she is expected to face President Trump, a Republican, in the November general election.
What is the second reaction?
Mr. Biden told the media on Friday that he had "no problem" with Bloomberg joining the democracy field.
"Michael is a solid guy," Biden said. "Let's see where it goes."
welcomed Mr. Bloomberg to the race on Twitter links to his own campaign website and suggested that the former mayor look at potential political plans.
In a tweet apparently directed at Mr Bloomberg,
Sanders wrote: "The billionaire class is scared and they should be scared."
Some recent opinion polls have suggested that Warren and Sanders – who are more politically liberal than Mr. Biden – may face an uphill battle against Trump.
The Republican National Committee said in a statement that the future entry of billionaires "underlines the weak field of democracy".
Chip Somodevilla / Getty Images
Bernie Sanders, Joe Biden and Elizabeth Warren are currently leading the field of Democratic candidates
Who is Bloomberg?
Mr. Bloomberg was a banker on Wall Street before continuing to create the financial publishing empire bearing his name.
His net worth is $ 52 billion (£ 40 billion), according to Forbes. This is 17 times more than Trump's (an estimated $ 3.1 billion).
Will US billionaires really pay more tax?
He organized a successful campaign for the mayor of New York in 2001, which remained for three consecutive years until 2013.
A philanthropist, he has donated millions of dollars to educational, medical and other causes.
Why is he driving now?
Analysis – Anthony Zurcher, BBC News, Washington
Why is he considering running for the highest political job in the country just a few months after he announced he would see 2020 from the sidelines?
Here are some theories:
Because he thinks he can win
Because he wants to shape the debate
Because he can afford
The best is the obvious answer. Bloomberg has plenty of pollsters and political strategists at his disposal and is reported to be a very computer-driven businessman. However, no advanced degree in quantitative analysis is required to realize that the democratic field, even at this (relatively) late date, is still in motion.
There are four candidates at or near the top of the early state and national primary polls – Joe Biden, Elizabeth Warren, Bernie Sanders and Pete Buttigieg. Of course, everyone has their strengths, but everyone also has obvious weaknesses.
Read Anthony & # 39; s works in full
What does Bloomberg believe?
Originally a Democrat, Mr. Bloomberg became the Republican to introduce his campaign for New York's mayor in 2001.
Now considered a moderate Democrat, he joined the party only last year.
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Michael Bloomberg has highlighted climate change and gun control as important issues
Mr. Bloomberg has liberal views on issues such as climate change, gun control, immigration and abortion rights.
He was credited this week with helping Democrats win control of the Virginia Legislature after his Gun Safety Everytown defense team for Gun Safety injected $ 2.5 million into the state election.
But Mr. Bloomberg is more conservative when it comes to subjects like finance and police work.
As mayor, he defended the New York Police Department's stop-and-frisk policy, which critics say disproportionately targeted African Americans and Latin Americans.
At the City Hall, Mr. Bloomberg banned supersize sodas to prevent obesity, but was overruled by the state's highest court.