Anar Mammadov was born on January 26, 1971, in Baku. In 1987 Anar entered the Azerbaijan State Medical University and graduated in 1994. The same year Anar was admitted to the law department of Baku State University, which he graduated in 1998. In 2000-2001, Mammadov studied at the "College of Petroleum Studies" (Oxford) in the educational program on oil supply, logistics and trading. Between 2012-2014, Anar enrolled to business management studies under the "TRIUM" international program of New York University, London School of Economics and "HEC Paris" ("TRIUM Global Executive MBA").

Anar’s business career started with "Avista" LLC., which he founded in 1995 and then continued between 1998-2007 at the international oil company "Milio" LLC, where he was a business development manager and regional director. From 2007-2009, Mammadov was the chief executive director to "Arxiel Carbonexis" LLC, and from 2009-2014 - the chief executive director of "SOCAR Georgia Gas" LLC. Between 2014-2016, Mammadov joined "SOCAR Energy Greece" S.A. as the chief executive officer. Since 2016, he worked as the chief executive director of the "Petkim" petrochemical complex in "SOCAR Türkiye", then in 2019 as the head of the Oil Refinery and Petrochemical Production Union, and since June 2, 2022, he was appointed an adviser to the president of SOCAR .

By the Decree of the President of the Republic of Azerbaijan Mr. Ilham Aliyev dated July 28, 2023, Anar Mammadov was appointed as the vice president of the State Oil Company of Azerbaijan Republic.

He is married and has three children.