His body was found when he did not appear for breakfast at ranch in West Texas, according to local reports.
KVIA, a TV station, said he had reported feeling unwell after a day of quail hunting on Friday.
He was a frequent source of frustration to liberals and last year issued a nine-page dissent when the court legalised same-sex marriave across the US, describing the majority decision as a “judicial Putsch” that posed a “threat to American democracy”.A conservative, he was appointed to the Supreme Court in 1986 by President Ronald Reagan.
Greg Abbott, the governor of Texas, was among the first to pay tribute.
“He was the solid rock who turned away so many attempts to depart from and distort the constitution,” he said. “We mourn his passing, and we pray that his successor on the Supreme Court will take his place as a champion for the written constitution and the rule of law.”
His death at a time when a Democratic president has regularly been thwarted by a Republican Congress will spark immediate speculation about who might replace him on the bench.
However – with an election due in November – there may not be enough time for Barack Obama to choose a liberal replacement.