The cuts equal more than a tenth of its workforce and will affect its UK headquarters and other countries.
Margherita Della Valle, who is Vodafone's finance director, said its "performance has not been good enough".
Vodafone has two headquarters in the UK, its head office in Reading and a group office in London's Paddington. The firm has already outlined plans to cut jobs in Germany and Italy.
Della Valle, who was appointed as Vodafone's new chief in January, said: "To consistently deliver, Vodafone must change. My priorities are customers, simplicity, and growth. We will simplify our organisation, cutting out complexity to regain our competitiveness."
It announced the job cuts after reporting a small rise in full-year sales to €45.7 billion and a fall in pre-tax profits.
It forecast earnings would be "broadly flat" for the current financial year.
Vodafone's former boss Nick Read stepped down in December amid concerns over the group's performance. He had unveiled plans to achieve around €1 billion of cost savings at the telecoms firm and warned that job cuts were likely.