The probe into the contaminated blood scandal will be a "full statutory inquiry" and will come under the responsibility of the Cabinet Office after victims and families "expressed strong views" over the potential involvement of the Department of Health, Downing Street said.
Prime Minister Theresa May announced earlier this year that an inquiry would be held into the events of the 1970s and 1980s, which left around 2,400 people dead.
But campaigners had rejected the Government's proposed process, saying the health department should not be involved in setting up an inquiry when it is under investigation itself.
Downing Street said there had been around 800 responses to the consultation in setting up the inquiry.
Thousands of haemophiliacs and other patients were given blood products infected with hepatitis C and HIV.
Campaigners and families of those affected by the scandal boycotted a meeting with Department of Health officials over the remit of the UK-wide inquiry earlier this year in protest at its involvement.
The Prime Minister's official spokesman said: "The inquiry will be conducted under the responsibility of the Cabinet Office rather than by the Department of Health with immediate effect.
"We have been absolutely clear of our determination to establish what happened in relation to the contaminated blood scandal of the 1970s and 1980s and to work with the families of those affected, and we are now moving forward with that process.
"There was a strong view that it should be done away from the Department of Health. We have listened to those views and that's why it will be conducted under the auspices of the Cabinet Office."
Families and victims had been asked whether they wanted a judge-led inquiry or a Hillsborough-style panel.
No 10 said there would be a further announcement by the end of the year on the setting up of the inquiry.