Rogers, who changed the London skyline with distinctive creations such as the Millennium Dome and The Leadenhall Building, known as the "Cheesegrater", "passed away quietly" on Saturday night, Freud communications agency's Matthew Freud said.
His son Roo Rogers also confirmed his death to The New York Times, but did not give the cause.
The Italian-born architect won a series of awards for his designs, including the 2007 Pritzker Architecture Prize, and is one of the pioneers of the "high-tech" architecture movement, distinguished by structures incorporating industrial materials such as glass and steel.
He is the co-creator of France's Pompidou Centre – opened in 1977 and famed for its multicoloured, pipe-covered facade – which he designed with Italian architect Renzo Piano.
Rogers' other well-known designs include Strasbourg's European Court of Human Rights, London’s Millennium Dome (now known as The O2) and the 3 World Trade Centre in New York, as well as international airport terminals in Madrid and London's Heathrow.
Born in Florence in 1933, his father was a doctor, his mother a former pupil of the famed Irish writer James Joyce. The family fled the dictatorship of Mussolini, settling in England in 1938.
Dyslexic and foreign to his schoolmates, he was bullied and beaten, and by 9 he considered hurling himself from his bedroom window, The New York Times writes in its profile. His learning disability was not widely understood or even recognised in those days; he was, he said, seen as stupid.
“People have asked me whether dyslexia makes you a better architect,” Rogers wrote in his memoir A Place for All People: Life, Architecture and the Fair Society, published in 2017. “I’m not sure whether that’s true, but it does rule out some careers, so it focuses you on what you can do.”
He left school in 1951 with no qualifications but managed to gain entry into London's Architectural Association School of Architecture, known for its modernism.
Rogers completed his architecture studies at Yale in the US in 1962, where he met fellow British architect Norman Foster.
Although buildings were Rogers' world, he insisted it was the space around them that was key in defining those that worked.
"The two can't be judged apart," he told The Guardian in 2017. "The Twin Towers in New York, for instance. They weren't great buildings, but the space between them was."
Rogers was knighted by Queen Elizabeth II in 1991.
– Additional reporting by AFP