The son of a wealthy landowner and a serf woman who was bonded to his estate, Morozov was born in the village of Borok in the Governorate of Yaroslavl.

In 1880, Olga Lyubatovich and Morozov left Narodnaya Volya and went to live in Geneva and London, where he was introduced to Karl Marx.

While in exile, Morozov wrote The Terrorist Struggle, a pamphlet that explained his views on how to achieve a democratic society in Russia.

This would also help to prevent a small group of leaders gaining power, forming oligarchical dictatorships after the overthrow of the Tsar.

During this period, he wrote political verse and began intense studies in the fields of physics, chemistry, astronomy, and history.

During World War I, Morozov went to the front in 1915 as a delegate of the All-Russian Zemstvo Union to aid the sick and wounded.

However, Anatoly Lunacharsky (Commissar for Education from 1917 to 1929) appointed him in 1918 to run the P. S. Lesgaft Institute of Natural Sciences [ru]) in Petrograd (Leningrad), a position which Morozov kept until his death at the age of 92.

In his declining years, Morozov established a laboratory in his native Borok, north of Uglich, to monitor and study "inland waters".

He had taken a sniper course in 1939 and claimed to be working on a new telescopic sight which needed field-testing, threatening that if he was not allowed to enlist he would ask Joseph Stalin himself to intervene.

He shot accurately despite needing glasses and, in one instance, spent half a day lying in ambush in the snow before killing a German officer.

He used his academic training to enhance his effectiveness as a sniper, studying the trajectory of his bullets and making adjustments for humidity and wind.