Rustam Ibrahimbeyov was born in Baku. He studied at the Azerbaijan State Institute of Oil and Chemistry (1962), the postgraduate course of the Institute of Cybernetics of the USSR Academy of Sciences, the script department of the Higher Courses of Directing and Screenwriting in Moscow (1967), and then the directing department (1974). He defended his candidate's thesis.

He wrote his first story, "Bread without Jam," in 1962. His plays "Sweetheart," "The Woman Behind the Green Door," "On His Own Path," "Contact," "House on the Sand," "Investigation," "Ultimatum," and "Burial in California" have been staged in more than 100 theaters around the world. In total, he has about 50 plays.

The film "Burnt by the Sun" (directed by Nikita Mikhalkov, Russia), for which he wrote the screenplay, was awarded the Academy Award of the American Film Academy (1994) and the Grand Jury Prize at the 47th Cannes International Film Festival.
The film "Urga - the Circle of Love" (1991, directed by Nikita Mikhalkov) was awarded the Golden Lion at the Venice Film Festival and the Felix Award in Berlin as the best European film. It was nominated for the Oscar as the best foreign film.
The film "East-West" (1999) was one of the candidates for the Oscar in the nomination for the best foreign film.
The film "White Sun of the Desert", based on his screenplay, was once the most watched film in the former USSR.
At the 48th International Antalya "Golden Orange" Film Festival (2011, Antalya / Turkey), Rustam Ibrahimbeyov was presented with the "Lifetime Honor Award". He received the “Golden Scythian Deer” award at the 41st International “Youth” Film Festival (2011, Kiev / Ukraine).

Honored Artist (1976), People's Writer (1998), Honored Artist of Russia (1995). He was awarded the State Prizes of Azerbaijan (1981), Russia (1993, 1995, 1997, 1999) and the USSR (1981). He is the only person to have been awarded the State Prize of Russia 3 times. He was awarded the Order of “Glory” by the President of the Republic of Azerbaijan (1999).
He is the founder of the “Ibrus” company, founded in 1989, and the “Ibrus” theater, which operated in Baku for a while. Rustam Ibrahimbeyov, Chairman of the Union of Cinematographers of Azerbaijan (1981-2022), Chairman of the Confederation of Unions of Cinematographers of the CIS and Baltic States (1992-2022), member of the European Academy of Cinematography (Felix), and the US Film Academy, died in Moscow in 2022 and was buried in the Alley of Honor in Baku.