Smirnov was the son of a worker and was born on 3 April 1916 in Kuznetsk, a town to the west of Samara, Russia, then part of Saratov province but now in Penza Oblast. He began his working life as an electrician in 1930 in Rostov-on-Don. He studied at the Novocherkassk Industrial Institute from 1933 to 1934 and graduated in 1939. Whilst studying, he worked from 1933 to 1930 in Novocherkassk, first as a duty electrician and then as an electrical engineering inspector.
Between 1939 and 1948, he rose from deputy head of production, to deputy chief of power, to being head of the Novocherkassk steam electric power plant. Smirnov became a member of the communist party in 1943.
From 1948 to 1949 he was at the Industry Academy of the Ministry of Armaments.
From 1949 to 1951 he was director of the Central Research Institute of Automatics and Hydraulics of the Ministry of Armaments.
From 1951 to 1952 he was head of rocket and space technology weapons of the Ministry of Armaments.
From 1952 to March 1961 he was director of the Dnipropetrovsk Machine-Building Factory - now called Yuzhmash. This enterprise started work on mass production of strategic military missiles in 1951, Once Smirnov was appointed in 1952, the factory began an active and hard work on the creation of 'vertical takeoff vehicles'. The first rockets completed were R-1 missiles assembled from components from other factories. But by November 1952 they were being mass-produced using components they made themselves. In 1953, the factory produced its first batch of liquid fuel rocket engines for anti-aircraft missiles, and completed the first fire tests of the engine. The factory was responsible for the beginning of series production of the R-12 missile; this was the missile used in the Cuban Missile Crisis. On 10 July 1959 the factory was awarded the Order of Lenin for creating the R-12 missile. The first successful launch of the R-16 intercontinental ballistic missile took place on 2 February 1961. The factory did not just make missiles. It also made tractors; in 1954 for example it produced 6,500. It played an important role in the life of Dnipropetrovsk; for example in 1957, it opened the Palace of Culture.
From 10 June 1961 to 13 March 1963 Smirnov was chairman of State Committee of the Council of Ministers of the USSR for Defence Technology with the rank of minister of the USSR.
From 13 March 1963 to 15 November 1985 he was deputy chairman of the Council of Ministers of the USSR.
As deputy chairman of the Council of Ministers, he was chairman of the Military Industrial Commission, reporting to Minister of Defence Dmitriy Ustinov. Smirnov retired in November 1985.