"He will be greatly missed, not only by his wife of 50 years, Marlene, and his three children, seven grandchildren and great grandchild, but also by his many thousands of readers and students around the world," a family statement said.
Hobsbawm won critical acclaim with a four-volume history of Europe in the 19th and 20th centuries, which was translated into 40 languages. His bestselling memoirs charted the pivotal moments in modern European history through which he lived.
Hobsbawm was born into a Jewish family at Alexandria, Egypt in the year of the Russian Revolution, 1917, and grew up in Vienna and Berlin before moving to London as a teenager in 1933 as Adolf Hitler was rising to power in Germany.
He joined the Communist party aged 14, and went on to be closely associated with Britain's left-wing Labour party, over which he was seen to have a strong influence in the 1980s and 1990s. He was once described by former Labour leader Neil Kinnock as "my favourite Marxist".
Hobsbawm maintained his commitment to Marxism even after the Soviet invasion of Hungary in 1956.
Years later he said he had "never tried to diminish the appalling things that happened in Russia", but had believed in the early days of the communist project that a new world was being born.