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.