Sir Martin Moore-Bick, 70, has spent more than 20 years as a judge of the Commercial Court and Court of Appeal until his retirement in December 2016.
Prime Minister Theresa May said "no stone will be left unturned" as part of a written statement informing lawmakers of the appointment.
"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,"she wrote.
Following that consultation, the judge will make a recommendation to the British prime minister.
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May said: "I will return to Parliament with the final terms of reference once this process has taken place. Then the inquiry will begin its work.
"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."
"It is vitally important that the inquiry be open, transparent and fair to all those whose involvement with Grenfell Tower comes under scrutiny. 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," he said.
However, the his appointment has faced some criticism over his history in housing related past judgements.
In 2014, he presided in an appeal court case and ruled in favour of Westminster City Council in a dispute over a tenant facing homelessness after refusing to be rehoused near Milton Keynes, miles away from London.
As he begins his inquiry, the Metropolitan Police investigation into the fire on June 14 has identified over 60 companies involved in the refurbishment of Grenfell Tower and said the probe is ongoing.
The Met Police said that while they are using "every imaginable source" to identify the victims of the fire, the final death toll is unlikely to be known before the end of the year.
Meanwhile, the number of high-rises across the UK that failed fire safety tests launched in the wake of the London tragedy stands at over 120 tower blocks.
An expert panel to advise on immediate safety action has been appointed following the safety failures.