Chowdhury was born in Chandpur District, in what is now Bangladesh. In college, he was involved in student politics. In 1962, he was elected to the Parliament of Pakistan, of which Bangladesh was then a part, as a member of the Awami League. When Sheikh Mujibur Rahman and other leaders of the Awami League were arrested in 1966, Chowdhury served as acting general secretary of the party until his own arrest in 1967. After his release he was active during Bangladesh's successful war for independence in 1971. After Bangladesh's independence, he was a longtime member of Parliament. He became information minister in Mujibur Rahman's cabinet in 1973, and following Mujubur's assassination in 1975, he left that position and led a faction of the Awami League.
During the early 1980s, Chowdhury supported the takeover of Hossain Mohammad Ershad and joined his Jatiya Party in 1984. He served as prime minister during Ershad's presidency for two years, from 1986 until he resigned in 1988. In 1990 Ershad's presidency ended. Chodhury rejoined the Awami League in 2001 and served as an advisor to the party until his death. He died in Bangladesh's capital Dhaka and was widely mourned by politicians of all the main parties.