The move comes two months after the chain, which has 578 UK stores, warned that 4,100 roles were at risk because of a need to reduce the number of back office jobs in favour of more customer-facing roles.
Asda chief executive Andy Clarke said: "Every supermarket must adapt to the intense changes in UK retailing or they will get left behind."
The new store structure will create 1,662 section managers and 4,000 section leaders but the redundancies will come from staff who do not meet the selection criteria or choose to leave.
Rival supermarket Morrisons made a similar announcement last month when it said it would axe 2,600 jobs in order to remove layers of management.
The big four supermarkets, including Tesco and Sainsbury's, are all being squeezed by discounters Aldi and Lidl and Waitrose at the upmarket end.
Asda said the new structure places a greater emphasis on e-commerce, puts more staff on the shop floor and removes back office administration tasks.
Mr Clarke said the restructuring was one of the most difficult decisions he has had to make as chief executive.
He added: "Whilst I genuinely believe that it is the right decision for the future of Asda, knowing that it will result in valued colleagues leaving us is not easy."
Mr Clarke said Asda first noticed "intense structural changes" in the market two year ago, since when the chain has examined its own set-up and tested scenarios before coming up with the proposals announced today.
Intense competition has dragged price inflation in the supermarket sector to its lowest level for almost eight years, according to Kantar Worldpanel.
The figure fell to 0.8% in the 12 weeks to June 22, according to its latest till-roll figures, which is the lowest level the research group has seen since it began collecting this data in October 2006.
Asda, which is part of US chain Wal-Mart, has shown signs that it is weathering the difficult conditions after Kantar said sales rose by 3.6% in the period, helping its market share lift to 17.1% from 16.9% a year earlier.