One of his first commissions was The Royal College of Physicians in Regent's Park in London, which was completed in 1964 and won international acclaim.
He was regarded as one of the greatest architects of the 20th century, even though some of his work attracted popular criticism.
The Prince of Wales described the landmark theatre as "a clever way of building a nuclear power station in the middle of London without anyone objecting".
Sir Denys' other famous designs include the University of East in Anglia in Norwich and the Royal College of Physicians in London.
He died on Thursday of pneumonia.
Sir Denys' influential career began in the 1930s.
Urban landscapes
He honed his craft with the Architectural Association School of Architecture and during World War II served with the Royal Engineers, earning an MBE.
He was later dubbed the "grandfather of modernism" as his designs were largely in concrete, with a principal theme being the idea of buildings as urban landscapes formed from interlocking spaces and levels.
One of his first commissions was The Royal College of Physicians in Regent's
Park in London, which was completed in 1964 and won international acclaim.
His next project was the University of East Anglia campus, completed in 1968, which included the striking "ziggurat" or pyramidal-shaped student halls.
In 1983 he designed the headquarters for the European Investment Bank in Luxembourg.
Influence
His most famous building, the National Theatre, which opened in 1976, may have attracted royal criticism but fellow architects were unanimous in their praise.
Sir Norman Foster described him as "a pioneer, a world-class architect who had tremendous influence".
Lord Rogers said: "The best of his buildings were recognised across the world."
Sir Denys, who was appointed CBE in 1965 and knighted in 1976, was married with three children.