Jejeebhoy was born in Bombay (now Mumbai) in 1783, the son of Merwanjee Mackjee Jejeebhoy and Jeevibai Cowasjee Jejeebhoy. His father was a textile merchant from Surat, Gujarat, who migrated to Bombay in the 1770s. Both of Jeejeebhoy's parents died in 1799, leaving the 16-year-old under the tutelage of his maternal uncle, Framjee Nasserwanjee Battliwala. At the age of 16, having had little formal education, he made his first visit to Calcutta and then began his first voyage to China to trade in cotton and opium.