Agha Mustafayev was born on 9 May 1942. In 1958, he entered  Azerbaijan State Medical University, Faculty of Pharmaceutics, graduating in 1963. From 1963 to 1966, he served as a chemist at Sumgayit Chemical Factory.

From 1966-1969, he did his postgraduate studies at ANAS Institute of Petrochemical Processes, where he served as a junior research fellow from 1969 to 1972. In 1972, he was transferred to ANAS Institute of Polymer Materials, working as a junior, senior and leading research fellow.

In 1997, he became head of the Department of Unsaturated Polyethers, and has headed Unsaturated Polyethers Laboratory since 2007. In 1971, he defended his PhD thesis, and achieved a ScD degree in 1991.

In 2007, Agha Mustafayev was made a professor of organic chemistry. From 1992 to 1998, he gave lectures in organic chemistry at Azerbaijan National Aristocratic University.

He has been a professor at the Department of Organic Chemistry, Baku State University, since 2001.

He is researching into effective ways of producing 5.5-dioxialkanetetrabrominecyclopentadienes, 5.5-alkanedioxitetrabrominespirocyclopentadienes on the basis of hexabrominecyclopentadienes, and studying diene synthesis reaction of these dienes with functional dienophiles.

He has published over 160 papers, and is the holder of 25 authorship certificates.

His papers have been featured in materials of international conferences held in the USA, United Kingdom, Czechoslovakia, Poland.  Agha Mustafayev has supervised five PhD students to completion. He is a member of D 02.011 Thesis Council under BSU.