The group, who have sold 70 million records, said Mr Corbyn had inspired young people and offered a "believable" alternative to business as usual.
Mr Corbyn has been backed by several stars, such as actor Daniel Radcliffe.
But best-selling Harry Potter author JK Rowling has called him a lousy leader.
Mr Corbyn is being challenged for the leadership by Owen Smith. The result of the election will be announced on 24 September.
The Labour leader, who has said he wants the arts to be a priority for the next Labour government, has received a number of celebrity endorsements in recent weeks.
Birmingham-based UB40, named after the then government's unemployment benefit form, were one of the most successful British groups of the 1980s and 1990s, notching up 50 hit singles - among them the chart toppers Red Red Wine, Can't Help Falling in Love and I Got You Babe.
Although three members of the original line-up have left in recent years, sparking a legal dispute over the use of the band's name, the remaining members led by guitarist and vocalist Robin Campbell have endorsed Mr Corbyn.
"Jeremy has re-ignited an interest in politics for people who no longer felt included, and engaged and inspired a new generation of young voters who, for the first time, believe that they have an incorruptible politician who truly represents them," Mr Campbell said.
Drummer Jimmy Brown said Mr Corbyn was the only frontline politician "willing to speak up for working people who have been badly treated by successive governments, including New Labour, in recent decades".
Mr Corbyn, who is opposed by the majority of his MPs and lost a vote of no confidence after the EU referendum, welcomed the band's backing ahead of a planned joint appearance on Tuesday.
"UB40's story was and remains inspiring; people from across cultures and backgrounds coming together and combining their talents - in a time when prejudice was more prevalent - and creativity to produce music that has endured across decades," he said.
As part of his arts manifesto released last month, Mr Corbyn pledged that all primary schools in England would get extra cash to fund arts activities and a single national scheme for arts scholarships would be set up.
The Labour leader told the Guardian on Monday he would be happy to meet JK Rowling to discuss their differences after she said he was taking the party in the wrong decision.
Her suggestion that Mr Corbyn risked destroying Labour and that the poorest in society need an "electable" alternative to the Conservatives not "mouthy, impotent socialism" provoked an angry response from Corbyn backers on social media.

No new date has yet been set for the game to be played.

Gregory died at hospital in Washington DC after being admitted with an undisclosed illness.
The family shared the news of their "enormous sadness" in a post on social media on Saturday.
From the 1960s Gregory mocked racism in his stand-up routines. He was among the first US black comedian to perform regularly in front of white audiences.
"It is with enormous sadness that the Gregory family confirms that their father, comedic legend and civil rights activist Mr Dick Gregory departed this earth tonight in Washington, DC," his son, Christian, wrote on Instagram.
He added that the family "appreciates the outpouring of support and love" but requested that their privacy be respected "during this very difficult time".
US civil rights activist Jesse Jackson paid tribute to Gregory on Twitter:
End of Twitter post  by @RevJJackson
Gregory was a no-holds-barred comedian, delivering lines in his performances that were likely to raise eyebrows.
"A Southern liberal?" he once said, "that's a guy that'll lynch you from a low tree".
"Segregation is not all bad," Gregory said on another occasion. "Have you ever heard of a collision where the people in the back of the bus got hurt?"
Gregory was also involved in a number of civil rights activities in the 1960s. He campaigned against the Vietnam War and his protests often involved hunger strikes.
British reggae band UB40 have praised Jeremy Corbyn as an "incorruptible politician" who will put working people first as they backed his campaign to remain as Labour leader.
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Saturday's Women's Super League 1 game between Doncaster Rovers Belles and Arsenal Ladies has been postponed because of a waterlogged pitch.
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US comedian and civil rights activist Dick Gregory has died at the age of 84, his family has announced.