Born in Kabul, Afghanistan. He gained a BSc in Mathemetics and Physics from the University of Kabul before leaving for Columbia University in New York where he received his Masters degree in 1957 (Pädagogik). Amin returned to Afghanistan in 1965 before completing his Ph.D to join the People's Democratic Party of Afghanistan (PDPA), he became a prominent member of the marxist Khalq (People) faction.
After the death of Mohammed Daoud Khan in 1978 the PDPA gained power with Noor Mohammad Taraki becoming President of the Democratic Republic of Afghanistan and secretary general of the PDPA while Amin and Babrak Karmal became deputy prime ministers. An attempt to institute Marxist-Leninist reforms provoked widespread resistance and a number of violent revolts, in February 1979 the U.S Ambassador Adolph Dubs was killed. the Khalq faction was gaining political power over the Parcham faction, with Karmal exiled to Europe Amin had gained considerable control by March 1979 and was named prime minister although Taraki retained his other posts. The unrest continued however and the regime was forced to seek more Soviet aid. On September 14, 1979 Taraki was killed in a confrontation between Taraki and Amin supporters and Amin then became the second President of the Democratic Republic of Afghanistan.
Amin worked to broaden his base of support and purged the PDPA of his perceived enemies. His regime was still under pressure from the insurgency in the country and he tried to gain Pakistani or America support and refused to take Soviet advice. This display of independent nationalism meant that when in December 1979, the Soviets began their invasion of Afghanistan, Amin and many of his followers were killed on December 27. Babrak Karmal became the next President.