Hall died on Monday at University College Hospital, London, surrounded by his family, the theatre said in a statement.
"Peter Hall was an internationally celebrated stage director and theatre impresario, whose influence on the artistic life of Britain in the 20th century was unparalleled," it added.
Hall's career spanned more than half a century. In his mid-20s he staged the English language premiere of Samuel Beckett's "Waiting for Godot" and in 1960, aged 29, he founded the Royal Shakespeare Company which he led until 1968.
Appointed Director of the National Theatre in 1973, Hall was responsible for the move from the Old Vic theatre to its current home in a purpose-built complex on the South Bank of the River Thames.
His work as a theatre director included the world premieres of Harold Pinter's "The Homecoming" (1965), Peter Shaffer’s "Amadeus" (1979) and the London and Broadway premieres of Alan Ayckbourn's "Bedroom Farce" (1977). His last production at the National Theatre was "Twelfth Night" in 2011.
Hall, who was diagnosed with dementia in 2011, was also an internationally renowned opera director and worked at many of the world’s leading houses including The Royal Opera, the Metropolitan Opera and Bayreuth where, in 1983, he staged Wagner's Ring Cycle to honour the 100th anniversary of the composer's death.
"We all stand on the shoulders of giants and Peter Hall’s shoulders supported the entirety of British theatre as we know it," said National Theatre director Rufus Norris in a statement.
"All of us, including those in the new generation of theatre-makers not immediately touched by his influence, are in his debt. His legendary tenacity and vision created an extraordinary and lasting legacy for us all."
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