The public services union said Yvette Cooper was its second choice.
Initially seen as an outsider in the contest, some bookmakers now make Mr Corbyn the favourite to replace Ed Miliband.
The BBC's Norman Smith said: "The Corbyn bandwagon rolls on."
He added: "What people thought was impossible, couldn't happen, wouldn't happen, may well happen."
Unison's endorsement does not mean its members who have chosen to be affiliated to Labour will necessarily vote for the Islington North MP, as they are free to cast their votes as they choose.
But it is seen as a blow to Andy Burnham, who had hoped for union backing for his campaign.
Sources in his campaign sought to present the decision as a setback for Mrs Cooper, who they said was confident of winning Unison's backing.
Liz Kendall is the other candidate in the contest.
At-a-glance profiles of the four contenders
Unison general secretary Dave Prentis said: "Jeremy Corbyn's message has resonated with public sector workers who have suffered years of pay freezes, redundancies with too many having to work more for less."
He told Channel 4 News nine of the union's 12 regions had nominated Mr Corbyn.
The union also said it would nominate Angela Eagle in the deputy leader contest, with Stella Creasy as its second choice.
Unison represents 1.3 million workers, including 28,000 Labour Party members and around 15,000 who are registered to vote in the leadership contest.
The third largest union, the GMB, has said it will make no formal recommendation.
Labour's new leader will be announced at a special conference on 12 September.
The popularity of Mr Corbyn's campaign has sparked a row within the party, with warnings from senior figures warning against a shift to the left.
Mr Corbyn, who topped a recent YouGov poll, has more nominations from local constituency parties than any other candidate, followed by Mr Burnham.
Although these nominations have no direct bearing on the result, they are seen as a useful indicator of the candidates' popularity among members.
Mr Burnham's team sought to counter the figures by releasing their own polling data suggesting their candidate is ahead by almost 10 points.
Mr Corbyn has said he only wants the backing of "genuine Labour" supporters after claims some "hard left" sympathisers and Conservatives were registering for Â£3 just in order to back him.
The party has played this down, saying careful checks are being made on everyone who has signed up.
But on Twitter, Croydon North MP Steve Reed said a Trade Union and Socialist Coalition candidate who stood against Labour in May had signed up, adding: "Hard left infiltrating Labour."

Shaun Coles, 24, of Church Street, Louth, admitted a charge of sexually assaulting a girl under the age of 13.
Lincoln Crown Court heard he and the girl had initially messaged each other on Facebook before meeting.
The messages between the two were uncovered by the girl's mother after she went missing. Coles was jailed for a total of 30 months.
Read more about this story and others from across Lincolnshire
The girl was meeting Coles and when she returned home she showed police messages between them on her phone.
Tony Standford, prosecuting, said: "Clearly there was a lot of inappropriate conversation and activity had taken place.
"There were numerous references to them being in love and to kissing and cuddling."
Coles admitted in police interviews he knew the girl was only 12 and that his behaviour was unacceptable.
Grace Hale, for the defence, described Coles as "very immature" and said he had issues with ADHD.
"He has been candid in his admissions to the police," she said.
"He had only known the girl for a short time before this incident.
Judge Michael Heath, imposing sentence, said: "You knew that she was 12 years old. You were twice her age.
"This was not the girl's fault. She was the victim and you should not have behaved in the way you did."
In addition to the jail term the judge also placed Coles on the sex offenders' register for life,
He was also given an indefinite sexual harm prevention order.
Left wing MP Jeremy Corbyn has the backing of the UK's two largest trade unions after Unison followed Unite in endorsing him to be Labour's next leader.
[NEXT_CONCEPT]
A man has been jailed for grooming a 12-year-old girl on Facebook who he went on to abuse.