The Grenfell Tower public inquiry will examine issues including the cause of the fire and the actions of authorities before the blaze, the Government has announced.
The Prime Minister said broader social questions provoked by the fire, which left at least 80 dead, will not form part of the inquiry but she was "determined" they would not be left "unanswered".
Sir Martin Moore-Bick, the retired judge leading the probe, will also scrutinise the "adequacy" of building regulations and the recent refurbishment of the block, the Government said.
Sir Martin suggested in a letter recommending the scope of the inquiry that wider consideration of social housing policy should not be included, despite the protestation of survivors.
But the Prime Minister was said to be "very clear" the omission of such problems would not mean they are left unanswered or seen as a lower priority.
Mrs May said: "It is vital that there is justice for the victims of this appalling tragedy and for their families who have suffered so terribly.
"The terms of reference set out by Sir Martin address crucial issues such as the cause of the fire and the adequacy of building and fire regulations which will allow the inquiry to get to the truth of what happened and learn the lessons to stop a similar catastrophe happening in the future.
"I am determined that the broader questions raised by this fire - including around social housing - are not left unanswered.
"We are taking action with the Housing Minister meeting social housing tenants to discuss the challenges they face and we will be setting out further proposals in due course."
The Prime Minister accepted in full the recommendations for the inquiry's scope made by former Court of Appeal judge Sir Martin in a letter last week.
With the terms of reference announced, the inquiry has officially begun and will hold its first hearing on September 14, with an initial report by Easter.
Survivors and campaigners had pressed for systemic issues underlying the cause of the tragedy on June 14 to be scrutinised.
Addressing these concerns, the Government said Housing Minister Alok Sharma will meet as many social tenants as possible both in the west London neighbourhood and across the country to build up a picture of the issues confronting them and work out a national approach.
Those touched by the disaster were urged to engage with the process so "as accurate a picture as possible" could be built.
The terms of reference were determined following consideration of more than 550 submissions.
Residents of the tower spent years chronicling a battle over safety issues with the Kensington and Chelsea Tenant Management Organisation (KCTMO), which ran the building.
A public blog, run by the Grenfell Action Group, alleged fire safety was being put unnecessarily at risk during a refurbishment of the 24-storey block.
During the £8.6 million renovation, new cladding with a flammable core was wrapped around the building, married with combustible insulation.
It is suspected the combination of these materials helped aid the spread of the inferno, which engulfed the building within minutes.
These issues will be a central consideration for Sir Martin's inquiry.