NHS England is expected to be brought back into the Department of Health within two years, while the cuts to integrated care boards (ICBs), which plan health services for individual regions, will reduce their headcounts by 50%.
NHS Providers' chief executive Daniel Elkeles said: "This is a pragmatic step that means planned redundancies can now go ahead.
"It reflects the flexibility of a three-year settlement, allowing some funding to be brought forward in order to generate future savings to go into front-line care.
"However, we must recognise the position of staff affected by these changes - people who have offered commitment and service to the NHS - who face a very uncertain future."
But Patricia Marquis of the Royal College of Nursing warned the redundancies could backfire.
"Front-line services need more investment, but to do this off the backs of making thousands of experts redundant is a false economy.
"Expert registered nurses working across NHS England and ICBs don't just run vital public health programmes and oversee care programmes for the vulnerable – they connect the NHS and social care services with one another.
"To imply these are administrators shows a complete lack of understanding of their roles and how they contribute to patient care."
