Residents and relatives of those killed have demanded answers as to why the fire spread so rapidly and whether proper fire safety measures had been in place.
"I am determined that there will be justice for all the victims of this terrible tragedy and for their families who have suffered so terribly," May said in a statement as she announced retired Court of Appeal judge Martin Moore-Bick would head the inquiry.
"We must get to the truth about what happened. No stone will be left unturned by this inquiry, but I have also been clear that we cannot wait for ages to learn the immediate lessons and so I expect the Chair will want to produce an interim report as early as possible."
Police have said exterior cladding which was added during a recent refurbishment failed all firesafety tests. Checks carried out since the fire have shown 137 other tower blocks had also failed tests, May's spokesman said on Thursday.
Moore-Bick said that the purpose of the inquiry would be to discover the truth about what happened.
"It is important for everyone that the inquiry should establish as quickly as possible the cause of the fire and how it was able to spread so quickly to the whole of the building," said Moore-Bick, who spent more than 20 years as a judge before retiring in December last year.
That ruling was overturned by the Supreme Court.
Families who survived the blaze at the Grenfell social housing block have expressed concerns that they will be rehoused away from the Kensington area in London.
The officer heading the police investigation said on Wednesday the final death toll from the firewould only be known after officers completed a painstaking search and recovery operation which could take until the end of the year.
(Reporting by Sarah Mills; Editing by Richard Balmforth and Toby Davis)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)