Sassoon was born in Baghdad; where his father; Saleh Sassoon; was a wealthy businessman and chief treasurer to the pashas (the governors of Baghdad) from 1781 to 1817; and leader of the city's Jewish community.

The family were Sephardim whose ancestors once lived in Spain. His mother was Amam Gabbai. After a traditional education in the Hebrew language; Sassoon married Hannah in 1818. They had two sons and two daughters before she died in 1826. Two years later he married Farha Hyeem (who was born in 1812 and died in 1886). The pair had six sons and three daughters.

Following increasing persecution of Baghdad's Jews by Daud Pasha; the family moved to Bombay via Persia. Sassoon was in business in Bombay no later than 1832; originally acting as a middleman between British textile firms and Gulf commodity merchants; subsequently investing in valuable harbour properties. His major competitors were Parsis; whose profits were built on their domination of the Sino-Indian opium trade since the 1820s.

When the Treaty of Nanking opened up China to British traders; Sassoon developed his textile operations into a profitable triangular trade: Indian yarn and opium were carried to China; where he bought goods which were sold in Britain; from where he obtained Lancashire cotton products. He sent his son Elias David Sassoon to Canton; where he was the first Jewish trader (with 24 Parsi rivals). In 1845 David Sassoon & Sons opened an office in what would soon become Shanghai's British concession; and it became the firm's second hub of operations.

In 1844; he set up a branch in Hong Kong; and a year later; he set up his Shanghai branch on the Bund to cash in on the opium trade. David Sassoon died in his country house in Pune in 1864. His business interests were inherited by his son Sir Albert Sassoon.