The U-turn comes days after victims were told that, unlike the victims and relatives of those killed in the Grenfell Tower fire, they would not receive financial support to help prepare for the inquiry.
Cabinet Office minister Chloe Smith informed MPs of the U-turn on Thursday, in response to an urgent question from Labour MP Diana Johnson in the House of Commons.
Earlier this week, victims told Sky News they were appalled and insulted that they would not receive support to help them inform the terms of reference of the public inquiry, which is due to begin later this year.
More than 7,500 people, the majority of them haemophiliacs, were infected with HIV and Hepatitis C by contaminated blood products in the 1970s and 1980s.
At least 2,400 have since died, in what has been described as the gravest scandal in NHS history.
Last year, the Prime Minister announced there would be a public inquiry, to be chaired by Justice Brian Langstaff.
Families and relatives have been seeking funding to cover legal advice during a consultation over the terms of reference of the inquiry, something that has been guaranteed to the Grenfell Tower victims.
Last week, the Cabinet Office informed them that they would not be eligible for funding as Grenfell was “exceptional”.
However, that decision has now been reversed.
Ms Smith told MPs: “The infected blood inquiry is a priority for this Government.
“The infected blood tragedy of the ’70s and ’80s should never have happened and the victims of this tragedy who have suffered so much pain and hardship deserve answers.
“I can confirm that ministers have decided that reasonable expenses, properly incurred in respect of legal representation for the purpose of responding to the consultation of the infected blood inquiry, on the terms of reference prior to the setting up date, will be awarded.
“It will be up to the solicitor to the inquiry to determine these. I hope that is good news to the House.”
Ms Johnson said the comparison with Grenfell Tower had been deeply hurtful to families.
“I welcome this decision, but wish that it had been made earlier,” she said.
“This is a group of people who have battled for many, many years to get to this inquiry and we want to make sure the terms of reference reflect all the concerns that they had.
“The letter of March 23, drafted by her [Ms Smith’s] civil servants, which tried to contrast Grenfell, which had been granted exceptional funding for the families, was somehow more deserving than this group of people and caused an enormous amount of hurt.
“Of course, we want to make sure the Grenfell families find out what happened, and 71 people died in that tragedy.
“But, in this case 2,400 people have already died and 70 have died since the inquiry was announced.”