Boris Johnson's spokesman said the PM had asked the Home Office and Department for Health to exempt NHS and care workers "as soon as possible".
Labour leader Sir Keir Starmer said it was "a victory for common decency".
The health immigration surcharge on non-EU migrants is £400 per year and set to rise to £624 in October.
The move to grant the exemption came after the PM's spokesman defended the fee earlier on Thursday.
Officials are now working on the detail and more will be announced "in the coming days".
But it is understood the plan will include exemptions for all NHS workers, including porters and cleaners, as well as independent health workers and social care workers.
The chief executive of the Royal College of Nursing, Dame Donna Kinnair, said the charge had created "an unfair and unjust financial burden", adding: "At last the government has agreed with us.
"This will ease the pressure on families who may be struggling financially or emotionally as a result."
Mr Johnson himself stood by the charge on Wednesday, telling MPs he "understood the difficulties faced by our amazing NHS staff", but said the government "must look at the realities" of funding the NHS.
It caused a backlash, with a number of Tory MPs joining opposition MPs in calling for him to reconsider - including the Tory chairman of the Commons public administration select committee, William Wragg, and his backbench colleague Sir Roger Gale.
Earlier, No 10 defended the levy, saying the money "goes directly back into the NHS to help save lives".
But now Mr Johnson's spokesman has said: "[The PM] has been thinking about this a great deal. He has been a personal beneficiary of carers from abroad and understands the difficulties faced by our amazing NHS staff.
"The purpose of the NHS surcharge is to benefit the NHS, help to care for the sick and save lives. NHS and care workers from abroad who are granted visas are doing this already by the fantastic contribution which they make."
The change was welcomed by Labour, as the party had been planning to seek an amendment to the Immigration Bill to secure the exemption.
Sir Keir tweeted: "Boris Johnson is right to have u-turned and backed our proposal to remove the NHS charge for health professionals and care workers.
"This is a victory for common decency and the right thing to do. We cannot clap our carers one day and then charge them to use our NHS the next."
Mr Wragg also praised the decision, saying the PM had "shown true leadership, listened and reflected".
The leader of the SNP in Westminster, Ian Blackford, said he was "pleased to see the change of heart after pressure", while the acting leader of the Liberal Democrats, Sir Ed Davey, called it "a great cross-party win".
The change was also welcomed by of Joint Council for the Welfare of Immigrants.
But the charity's chief executive Satbir Singh added: "It's depressing that it's taken nearly two months for the government to listen."
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