New chief executive Noel Quinn gave the news to his 235,000 staff around the globe in a memo seen by the BBC and confirmed as authentic by the bank.
The lender had originally announced the plan in February, but put it on hold amid the coronavirus pandemic.
HSBC said it would try to find internal jobs for those affected but that redundancies were likely.
In April, the bank had said it would hold fire on the cuts, explaining that it did not want to leave staff unable to find work elsewhere during the coronavirus outbreak.
The move is part of a restructuring programme which aims to achieve $4.5bn (£3.6bn) of cost cuts by 2022.
Some cuts are likely to come from merging support roles in the commercial bank and investment bank. The bank will also review less-profitable areas of business.