The union said the "disgraceful" move in the lead-up to Christmas would boost the bank's "massive profits".
Jobs will go across several back-office divisions, including compliance, finance, legal, policy, IT and risk, according to Unite.
Barclays has not confirmed numbers, but said it was taking action to "simplify the business".
Affected staff were told at lunchtime on Tuesday, Unite said.
It said it was pressing Barclays to avoid all compulsory redundancies and redeploy staff in the impacted areas of the business.
The union said it had secured improved payments and support for affected workers, including those with less than two years' service.
But a spokesperson for Barclays said the cuts had been outlined in its third-quarter results in October.
Barclays chief executive CS Venkatakrishnan said at the time that the bank saw "further opportunities to enhance returns for shareholders through cost efficiencies and disciplined capital allocation across the group".
Speaking on Tuesday, a bank spokesperson confirmed it was making changes to its headcount, "as management layers are reduced and the group improves its technology and automation capabilities.
"We are committed to supporting impacted colleagues through these changes."
But Unite general secretary Sharon Graham said: "Barclays is disgracefully cutting jobs to further boost its massive profits. This is a mega-rich bank that is already on course to make eye-watering profits this year."
The bank reported pre-tax profits for the three months to September of £1.9bn, slightly better than analysts' forecasts, but down from £2bn a year ago.
Barclays has cut costs in the last few years, and has already seen jobs go across its retail and investment banking businesses.
It has also announced nearly 200 branch closures in recent years, saying only 10% of transactions were now taking place face-to-face.
The group had around 22,300 staff in total at the end of last year.
The cuts come as reports suggest up to 2,500 jobs are at risk at another High Street bank, Lloyds.
According to the Guardian, the bank is ready to start a consultation with staff in several roles, including analysts and product managers, as part of a shake-up.
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