Families and victims had been asked whether they wanted a judge-led inquiry or a Hillsborough-style panel.
Downing Street had then indicated there would be a further announcement by the end of this year confirming what form the inquiry would take.
A spokesman for the prime minister said: “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.”
The decision was made after a public consultation received more than 800 responses.