In 1959, Prokhorov became a professor at Moscow State University – the most prestigious university in the Soviet Union; the same year, he was awarded the Lenin Prize. In 1960, he became a member of the Russian Academy of Sciences and elected Academician in 1966. In 1967, he was awarded his first Order of Lenin (he received five of them during life, in 1967, 1969, 1975, 1981 and 1986). In 1968, he became vice-director of the Lebedev Institute and in 1971 took the position of Head of Laboratory of another prestigious Soviet institution, the Moscow Institute of Physics and Technology. In the same year, he was elected a member of the American Academy of Arts and Sciences. In 1983 he was elected a Member of the German Academy of Sciences Leopoldina. Between 1982 and 1998, Prokhorov served as acting director of the General Physics Institute of the Russian Academy of Sciences, and after 1998 as honorary director. After his death in 2002, the institute was renamed the  of the Russian Academy of Sciences. Prokhorov was a Member and one of the Honorary Presidents of the International Academy of Science, Munich and supported 1993 the foundation and development of the Russian Section of International Academy of Science, Moscow.
In 1969, Prokhorov became a Hero of Socialist Labour, the highest degree of distinction in the Soviet Union for achievements in national economy and culture. He received the second such award in 1986. Starting in 1969, he was the chief editor of the Great Soviet Encyclopedia. He was awarded the Frederic Ives Medal, the highest distinction of the Optical Society of America (OSA), in 2000 and became an Honorary OSA Member in 2001. The same year, he was awarded the Demidov Prize.
He died on 8 January 2002 at Moscow and was buried at Novodevichy Cemetery.