Andrew Lansley, who has lost his role as Health Secretary in the Government cabinet reshuffle, was described by a union chief as one of the worst health secretaries since the NHS was formed in 1948.
Jeremy Hunt, who came under huge pressure as Culture Secretary earlier this year over his role in the BSkyB takeover bid, was appointed Health Secretary by Prime Minister David Cameron.
Mr Lansley was moved to Commons leader.
Health workers' union Unite said the departure of the "disastrous" Mr Lansley gives an opportunity for a "complete rethink" on the future of the health service.
The union's head of health, Rachael Maskell, said: "The NHS has been pushed to the brink of destruction by Andrew Lansley - a minister who simply would not listen either to the patients or the professionals. Jeremy Hunt must reflect deep and hard on the errors of his predecessor and seek immediate dialogue with the NHS team and their unions.
"He has the power to slam the door on the increasing privatisation of the NHS.
"Andrew Lansley must rank as one of the worst health secretaries since the NHS was formed in 1948.
"He presided over deeply unpopular bungled reforms which heralded rising waiting lists, £20 billion cuts to services, job losses to thousands of nurses and other health workers, installed an expensive, needless bureaucracy and announced an open sesame to the private firms which put profit before patient care.
"He was also responsible for dramatic cuts to pay and pensions, as well as long-established terms and conditions. NHS staff have had their morale crushed by Lansley's unlistening and steamroller mindset.
"David Cameron may have shunted him elsewhere, but serious work is needed now to repair the dreadful damage wrought by Lansley and his policies."
Peter Carter, general secretary of the Royal College of Nursing, said: "In challenging times for the health service, the RCN has not seen eye to eye with Andrew Lansley on the Government's health reforms.
"The RCN will now be looking to work with incoming Secretary of State Jeremy Hunt to ensure that the nursing voice is heard.
"There are profound challenges facing health in the UK, such as the need to save £20 billion from across the NHS in England, staff being asked to do more with less, waiting lists lengthening and waiting times rising, threats to public health, the delivery of social care to an ageing population, and the demands of shifting care from hospitals into the community and an unnecessary shift to regional pay."
Unison's head of health, Christina McAnea said: "The coalition Government presided over the most damaging piece of legislation that the NHS has ever seen in the Health and Social Care Act, and this will be Andrew Lansley's legacy.
"Changing the name over the door will not change our opinion of the Act. It is about policies, not personalities, and our opposition will continue as long as this coalition's assault on our NHS persists.
"Jeremy Hunt has an opportunity to listen to patients, professionals and unions about the damage the Act will continue to do to the NHS, let's hope he does not waste it."