Ms Long-Bailey, a frontrunner in the race to replace Jeremy Corbyn, needs the backing of one more Labour affiliate to secure a place on the ballot paper.
She was endorsed by the Bakers, Food and Allied Workers’ Union last week.
Unite will also back Richard Burgon for deputy leader.
Mr McCluskey said Ms Long-Bailey has the “brains and the brilliance” to beat Boris Johnson and is the “candidate best placed to take the fight to the Tory Party on behalf of Unite members and their communities”.
“She is standing for unity, socialism and the determination to make Johnson’s term in office short-lived,” he added.
“Unite is also confident that Richard will make a superb deputy to Becky, displaying the qualities that have long been absent from that post – pride in our values, a passion for our party to succeed and, above all, loyalty to their leader.”
Candidates are required to have won the nomination of three Labour affiliates, including at least two unions, which amount to at least 5 per cent of affiliate members.
The only other route on to the ballot is by receiving nominations from at least 5 per cent of constituency Labour parties (CLPs).
Shadow Brexit secretary Sir Keir Starmer and Wigan MP Lisa Nandy have already made it through the nomination process, and Ms Long-Bailey is widely expected to join them in the coming weeks.
Shadow foreign secretary Emily Thornberry also hopes to be in the final stage of the contest.
Earlier in the day, Labour announced it had cancelled its leadership hustings in Leeds on Saturday after Sir Keir pulled out as his mother-in-law is critically ill in hospital.
He said on Thursday that he was suspending campaigning after his mother-in-law was involved in a serious accident.
General secretary Jennie Formby said that to ensure fairness to all the candidates, the party’s procedures committee had agreed Saturday’s hustings should not now go ahead.
The deputy leadership hustings will take place as planne